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All Textbook Solutions for College Algebra

For the following exercises, use any method to solve the nonlinear system. x2y2=9x=3 For the following exercises, use any method to solve the nonlinear system. x2y2=9y=3 For the following exercises, use any method to solve the nonlinear system. x2y2=9xy=0 For the following exercises, use any method to solve the nonlinear system. x2+y=24x+y=1 For the following exercises, use any method to solve the nonlinear system. x2+y=22y=x For the following exercises, use any method to solve the nonlinear system. x2+y2=25x2y2=36 For the following exercises, use any method to solve the nonlinear system. x2+y2=1y2=x2 For the following exercises, use any method to solve the nonlinear system. 16x29y2+144=0y2+x2=16 For the following exercises, use any method to solve the nonlinear system. 3x2y2=12(x1)2+y2=1 For the following exercises, use any method to solve the nonlinear system. 3x2y2=12(x1)2+y2=4 For the following exercises, use any method to solve the nonlinear system. 3x2y2=12x2+y2=16 For the following exercises, use any method to solve the nonlinear system. x2y26x4y11=0x2+y2=5 For the following exercises, use any method to solve the nonlinear system. x2+y26y=7x2+y=1 For the following exercises, use any method to solve the nonlinear system. x2+y2=6xy=1 For the following exercises, graph the inequality. x2+y9 For the following exercises, graph the inequality. x2+y24 For the following exercises, graph the system of inequalities. Label all points of intersection. x2+y1y2x For the following exercises, graph the system of inequalities. Label all points of intersection. x2+y5y5x+10 For the following exercises, graph the system of inequalities. Label all points of intersection. 43. x2+y2253x2y212 For the following exercises, graph the system of inequalities. Label all points of intersection. 44. x2y24x2+y212 For the following exercises, graph the system of inequalities. Label all points of intersection. x2+3y2163x2y21 For the following exercises, graph the inequality. yexyln(x)+5 For the following exercises, graph the inequality. ylog(x)yex For the following exercises, find the solutions to the nonlinear equations with two variables. 4x2+1y2=245x22y2+4=0 For the following exercises, find the solutions to the nonlinear equations with two variables. 6x21y2=81x26y2=18 For the following exercises, find the solutions to the nonlinear equations with two variables. x2xy+y22=0x+3y=4 For the following exercises, find the solutions to the nonlinear equations with two variables. x2xy2y26=0x2+y2=1 For the following exercises, find the solutions to the nonlinear equations with two variables. x2+4xy2y26=0x=y+2 For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. 53. xy1yx For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. 54. x2+y3y2x For the following exercises, construct a system of nonlinear equations to describe the given behaviour, then solve for the requested solutions. 55. Two numbers add up to 300. One number is twice the square of the other number. What are the numbers?For the following exercises, construct a system of nonlinear equations to describe the given behaviour, then solve for the requested solutions. 56. The squares of two numbers add to 360. The second number is half the value of the first number squared. What are the numbers?For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. 57. A laptop company has discovered their cost and revenue functions for each day: C(x)=3x210x+200 and R(x)=2x2+100x+50 . If they want to make a profit, what is the range of laptops per day that they should produce? Round to the nearest number which would generate profit.For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. 58. A cell phone company has the following cost and revenue functions: C(x)=8x2600x+21,500 and R(x)=3x2+480x . What is the range of cell phones they should produce each day so there is profit? round to the nearest number that generates profit.Find the partial fraction decomposition of the following expression. x(x3)(x2)Find the partial fraction decomposition of the expression with repeated linear factors. 6x11(x1)2 Find the partial fraction decomposition of the expression with a nonrepeating irreducible quadratic factor. 5x26x+7(x1)(x2+1)Find the partial fraction decomposition of the expression with a repeated irreducible quadratic factor. x34x2+9x5(x22x+3)2 Can any quotient of polynomials be decomposed into at least two partial fractions? If so, explain why, and if not, give an example of such a fraction Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of equations.)Can you explain how to verify a partial fraction decomposition graphically?You are unsure if you correctly decomposed the partial fraction correctly. Explain how you could double check your answer.Once you have a system of equations generated by the partial fraction decomposition, can you explain another method to solve it? For example if you had 7x+133x2+8x+15=Ax+1+B3x+5 , we eventually 7x+13=A(3x+5)+B(x+1) .Explain how you could intelligently choose an x-value that will eliminate either A or B and solve for A and B.For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 5x+16x2+10x+24 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 7. 3x79x25x24 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. x24x22x24 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 10x+47x2+7x+10 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. x6x2+25x+25 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 32x1120x213x+2 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. x+1x2+7x+10 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 5xx29 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 10xx225 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 6xx24 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 2x3x26x+5 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 4x1x2x6 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 4x+3x2+8x+15 For the following exercises, find the decomposition of the partial fraction for the nonrepeating linear factors. 3x1x25x+6 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 5x19(x+4)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. x(x2)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 7x+14(x+3)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 24x27( 4x+5)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 24x27( 6x7)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 5x( x7)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 5x+142x2+12x+18 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 5x2+20x+82x(x+1)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 4x2+55x+255x(3x+5)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. 29. 54x3+127x2+80x+162x2(3x+2)2 For the following exercises, find the decomposition of the partial fraction for the repeating linear factors. x35x2+12x+144x2(x2+12x+36)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2+6x+11(x+2)(x2+x+3)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2+9x+23(x1)(x2+6x+11)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 2x2+10x+4(x1)(x2+3x+8)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. x2+3x+1(x+1)(x2+5x2)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2+17x1(x+3)(x2+6x+1)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2(x+5)(x2+7x5)For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2+5x+3x31 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 5x2+18x4x3+8 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 39. 3x27x+33x3+27 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. x2+2x+40x3125 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 4x2+4x+128x327 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 50x2+5x3125x31 For the following exercises, find the decomposition of the partial fraction for the irreducible non repeating quadratic factor. 2x330x2+36x+216x4+216x For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factors. 3x3+2x2+14x+15(x2+4)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x3+6x2+5x+9(x2+1)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x3x2+x1(x23)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x2+5x+5(x+2)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x3+2x2+4x(x2+2x+9)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x2+25(x2+3x+25)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 2x3+11x+7x+70(2x2+x+14)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 5x+2x(x2+4)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. x4+x3+8x2+6x+36x(x2+6)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 2x9(x2x)2 For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. 5x32x+1(x2+2x)2 For the following exercises, find the partial fraction expansion. x2+4(x+1)3 For the following exercises, find the partial fraction expansion. x34x2+5x+4(x2)3 For the following exercises, perform the operation and then find the partial fraction decomposition. 7x+8+5x2x1x26x16 For the following exercises, perform the operation and then find the partial fraction decomposition. 1x43x+62x+7x2+2x24 For the following exercises, perform the operation and then find the partial fraction decomposition. 2xx21612xx2+6x+8x5x24x Add matrix A and matrix B. A=[211603] and B=[314253]Given matrix B, find - 2B where A=[4132]Can we add any two matrices together? If so, explain why; if not, explain why not and give an example of two matrices that cannot be added together.Can we multiply any column matrix by any row matrix? Explain why or why not.Can both the products AB and BA be defined? If so, explain how; if not, explain why.Can any two matrices of the same size be multiplied? If so, explain why, and if not, explain why not and give an example of two matrices of the same size that cannot be multiplied together.Does matrix multiplication commute? That is, does AB=BA ? If so, prove why it does. If not, explain why it does not.For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] A + B For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] C+D For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] A+ C For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] B-E For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] C + F For the following exercises, use the matrices below and perform the matrix addition or subtraction. Indicate if the operation is undefined. A=[1307],B=[214226],C=[18125926],D=[107514261],E=[612145],F=[078159174] D-B For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] 5A For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] 3B For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] -2B For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] -4C For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] 12 C For the following exercises, use the matrices below to perform scalar multiplication. A=[461312],B=[321091264],C=[ 16 3 7 18 90 5 3 29],D=[18121381467421] 100D For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] AB For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] BC For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] CA For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] BD For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] DC For the following exercises, use the matrices below to perform matrix multiplication. A=[1532],B=[ 3 6 4 8 0 12],C=[4251069],D=[23129310810] CB For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 24. A+BC For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 25. 4A+5D For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 26. 2C+B For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 27. 3D+4E For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 28. C0.5D For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. A=[2567],B=[9642],C=[0971],D=[875432092],E=[453765109] 29. 100D10E For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 30. AB For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 31. BA For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 32. CA For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 33. BC For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 34. A2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 35. B2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 36. C2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 37. B2A2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 38. A2B2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 39. (AB)2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1020525],B=[40102030],C=[101010] 40. (BA)2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 41. AB For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 42. BA For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 43. BD For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 44. DC For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 45. D2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 46. A2 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 47. D3 For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 48. (AB)C For the following exercises, use the matrices below to perform the indicated operation if possible. if not possible, explain why the operation cannot be performed. (Hint: A2=AA ) A=[1023],B=[234115],C=[0.510.50.10.20.3],D=[101675421] 49. A(BC)For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. A=[2091830.545],B=[0.530416872],C=[101010101] 50. AB For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. A=[2091830.545],B=[0.530416872],C=[101010101] 51. BA For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. A=[2091830.545],B=[0.530416872],C=[101010101] 52. CA For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. A=[2091830.545],B=[0.530416872],C=[101010101] 53. BC For the following exercises, use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. A=[2091830.545],B=[0.530416872],C=[101010101] 54. ABC For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B=[100001010] 55. B2 For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B=[100001010] 56 B3 For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B=[100001010] 57. B4 For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B=[100001010] 58. B5 For the following exercises, use the matrix below to perform the indicated operation on the given matrix. B=[100001010] 59. Using the above questions, find a formula for Bn . Test the formula for B201andB202 , using a calculator.Write the augmented matrix of the given system of equations. 4x3y=113x+2y=4 Write the system of equations from the augmented matrix. [111213011|519]Solve the given system by Gaussian elimination. 4x+3y=11x3y=1 Write the system of equations in row-echelon form. x2y+3z=9x+3y=42x5y+5z=17 Solve the system using matrices. x+4yz=42x+5y+8z=15x+3y3z=1 A small shoe company took out a loan of $l,500,000 to expand their inventory. Part of the money was borrowed at 7% part was borrowed at 8% and part was borrowed at 10%.Theamount borrowed at 10% was four times the amount borrowed 7% and the annual interest on all three loans was $130,500. Use matrices to find the amount borrowed at each rate.Can any system of linear equations be written as an augmented matrix? Explain why or why not. Explain how to write that augmented matrix.Can any matrix be written as a system of linear equations? Explain why or why not. Explain how to write that system of equations.Is there only one correct method of using row operations on a matrix? Try to explain two different row operations possible to solve the augmented matrix [9312|06] .Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?Can a matrix that has 0 entries for an entire row have one solution? Explain why or why not.For the following exercises, write the augmented matrix for the linear system. 8x37y=82x+12y=3 For the following exercises, write the augmented matrix for the linear system. 16y=49xy=2 For the following exercises, write the augmented matrix for the linear system. 3x+2y+10z=36x+2y+5z=134x+z=18 For the following exercises, write the augmented matrix for the linear system. x+5y+8z=1912x+3y=43x+4y+9z=7 For the following exercises, write the augmented matrix for the linear system. 6x+12y+16z=419x5y+3z=9x+2y=8 For the following exercises, write the linear system from the augmented matrix. [ 256 18|526]For the following exercises, write the linear system from the augmented matrix. [34 10 17|10439]For the following exercises, write the linear system from the augmented matrix. [320 1 94857|318]For the following exercises, write the linear system from the augmented matrix. . [8 291 175003|433810]For the following exercises, write the linear system from the augmented matrix. [45 201 5887 3|1225]For the following exercises, solve the system by Gaussian elimination. [1000|30]For the following exercises, solve the system by Gaussian elimination. [1010|12]For the following exercises, solve the system by Gaussian elimination. [1245|36]For the following exercises, solve the system by Gaussian elimination. [ 124 5|36]For the following exercises, solve the system by Gaussian elimination. [ 2002|11]For the following exercises, solve the system by Gaussian elimination. 2x3y=95x+4y=58 For the following exercises, solve the system by Gaussian elimination. 6x+2y=43x+4y=17 For the following exercises, solve the system by Gaussian elimination. 2x+3y=124x+y=14 For the following exercises, solve the system by Gaussian elimination. 4x3y=23x5y=13 For the following exercises, solve the system by Gaussian elimination. 5x+8y=310x+6y=5 For the following exercises, solve the system by Gaussian elimination. 3x+4y=126x8y=24 For the following exercises, solve the system by Gaussian elimination. 60x+45y=1220x15y=4 For the following exercises, solve the system by Gaussian elimination. 11x+10y=4315x+20y=65 For the following exercises, solve the system by Gaussian elimination. 29. 2xy=23x+2y=17 For the following exercises, solve the system by Gaussian elimination. 1.06x2.25y=5.515.03x1.08y=5.40 For the following exercises, solve the system by Gaussian elimination. 34x35y=414x+23y=1 For the following exercises, solve the system by Gaussian elimination. 32. 14x23y=112x+13y=3 For the following exercises, solve the system by Gaussian elimination. [100011001|314587]For the following exercises, solve the system by Gaussian elimination. [101110011|502090]For the following exercises, solve the system by Gaussian elimination. [123056008|479]For the following exercises, solve the system by Gaussian elimination. [ 0.1 0.3 0.1 0.4 0.2 0.1 0.6 0.1 0.7|0.20.80.8]For the following exercises, solve the system by Gaussian elimination. 2x+3y2z=34x+2yz=94x8y+2z=6 For the following exercises, solve the system by Gaussian elimination. x+y4z=45x3y2z=02x+6y+7z=30 For the following exercises, solve the system by Gaussian elimination. 39. 2x+3y+2z=14x6y4z=210x+15y+10z=5 For the following exercises, solve the system by Gaussian elimination. x+2yz=1x2y+2z=23x+6y3z=5 For the following exercises, solve the system by Gaussian elimination. x+2yz=1x2y+2z=23x+6y3z=3 For the following exercises, solve the system by Gaussian elimination. x+y=2x+z=1yz=3 For the following exercises, solve the system by Gaussian elimination. x+y+z=100x+2z=125y+2z=25 For the following exercises, solve the system by Gaussian elimination. 14x23z=1215x+13y=4715y13z=29 For the following exercises, solve the system by Gaussian elimination. 12x+12y+17z=531412x12y+14z=314x+15y+13z=2315 For the following exercises, solve the system by Gaussian elimination. 12x13y+14z=29615x+16y17z=43121018x+19y+110z=4945 For the following exercises, Gaussian elimination to solve the system. 47. x17+y28+z34=0x+y+z=6x+23+2y+z33=5 For the following exercises, Gaussian elimination to solve the system. 48. x14y+14+3z=1x+52+y+74z=4x+yz22=1 For the following exercises, Gaussian elimination to solve the system. 49. x34y13+2z=1x+52+y+52+z+52=8x+y+z=1 For the following exercises, Gaussian elimination to solve the system. 50. x310+y+322z=3x+54y18+z=32x14+y+42+3z=32 For the following exercises, Gaussian elimination to solve the system. 51. x34y13+2z=1x+52+y+52+z+52=7x+y+z=1 For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 52. Every day, a cupcake store sells 5,000 cupcakes in chocolate and vanilla flavors. If the chocolate flavor is 3 times as popular as the vanilla flavor, how many of each cupcake sell per day?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 53. At a competing cupcake store, $4,520 worth of cupcakes are sold daily. The chocolate cupcakes cost $2.25 and the red velvet cupcakes cost $1.75. If the total number of cupcakes sold per day is 2,200, how many of each flavor are sold each day?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 54. You invested $10,000 into two accounts: one that has simple 3% interest, the other with 2.5% interest. If our total interest payment after one year was $283.50, how much was in each account after the year passed?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 55. You invested $2,300 into account 1, and $2,700 into account 2. If the total amount of interest after one year is $254, and account 2 has 1.5 times the interest rate of account 1, what are the interest rates? Assume simple interest rates.For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 56. Bikes’R’Us manufactures bikes, which sell for $250. It costs the manufacturer $180 per bike, plus a startup fee of $3,500. After how many bikes sold will the manufacturer break even?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 57. A major appliance store is considering purchasing vacuums from a small manufacturer. The store would be able to purchase the vacuums for $86 each, with a delivery fee of $9,200, regardless of how many vacuums are sold. If the store needs to start seeing a profit after 230 units are sold, how much should they charge for the vacuums?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 58. The three most popular ice cream flavors are chocolate, strawberry, and vanilla, comprising 83% of the flavors sold at an ice cream shop. If vanilla sells 1% more than twice strawberry, and chocolate sells 11% more than vanilla, how much of the total ice cream consumption are the vanilla, chocolate, and strawberry flavors?For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 59. At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up 12% of total ice cream sales. This year, the same three ice creams made up 16.9% of ice cream sales. The rocky road sales doubled, the banana sales increased by 50%, and the pumpkin sales increased by 20%. If the rocky road ice cream had one less percent of sales than the banana ice cream, find out the percentage of ice cream sales each individual ice cream made last year.For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 60. A bag of mixed nuts contains cashews, pistachios, and almonds. There are 1,000 total nuts in the bag, and there are 100 less almonds than pistachios. The cashews weigh 3 g, pistachios weigh 4 g, and almonds weigh 5 g. If the bag weighs 3.7 kg, find out how many of each type of nut is in the bag.For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. 61. A bag of mixed nuts contains cashews, pistachios, and almonds. Originally there were 900 nuts in the bag. 30% of the almonds, 20% of the cashews, and 10% of the pistachios were eaten, and now there are 770 nuts left in the bag. Originally, there were 100 more cashews than almonds. Figure out how many of each type of nut was in the bag to begin with.Show that the following two matrices are inverses of each other. A=[1413],B=[3411]Use the formula to find the inverse of matrix A. Verify your answer by augmenting with the identity matrix. A1=[1123]Find the inverse of the 33 matrix. A=[217111117032]Solve the system using the inverse of the coefficient matrix. 2x17y+11z=0x+11y7z=83y2z=2 In a previous section, we showed that matrix multiplication is not commutative, that is, ABBA in most cases. Can you explain why matrix multiplication is commutative for matrix inverses, that is, A1A=AA1 ?Does every 22 matrix have an inverse? Explain why or why not. Explain what condition is necessary for an inverse to exist.Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?Can a matrix with an entire column of zeros have an inverse? Explain why or why not.Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.In the following exercises, show that matrix A is the inverse of matrix B. A=[1011],B=[1011]In the following exercises, show that matrix A is the inverse of matrix B. A=[1234],B=[21 3 2 1 2]In the following exercises, show that matrix A is the inverse of matrix B. A=[4570],B=[0 1 7 1 5 4 35]In the following exercises, show that matrix A is the inverse of matrix B. A=[2 1 231],B=[2164]In the following exercises, show that matrix A is the inverse of matrix B. 10. A=[101011011],B=12[211011011]In the following exercises, show that matrix A is the inverse of matrix B. A=[123402169],B=14[60217351224]In the following exercises, show that matrix A is the inverse of matrix B. A=[3821115612],B=136[684672611225]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [3219]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [2231]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [3792]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [4358]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [1122]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [0110]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [0.51.510.5]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [106217302]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [013410105]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [121341245]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [193256427]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [1234812142]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [ 1 2 1 2 1 2 1 3 1 4 1 5 1 6 1 7 1 8]For the following exercise, find the multiplicative inverse of each matrix, if it exist. [123456789]For the following exercise, solve the system using the inverse of a 22 matrix 27. 5x6y=614x+3y=2 For the following exercise, solve the system using the inverse of a 22 matrix 28. 8x+4y=1003x4y=1 For the following exercise, solve the system using the inverse of a 22 matrix 29. 3x2y=6x+5y=2 For the following exercise, solve the system using the inverse of a 22 matrix 30. 5x4y=54x+y=2.3 For the following exercise, solve the system using the inverse of a 22 matrix 31. 3x4y=912x+4y=6 For the following exercise, solve the system using the inverse of a 22 matrix 32. 2x+3y=310x+5y=12 For the following exercise, solve the system using the inverse of a 22 matrix 33. 85x45y=2585x+15y=710 For the following exercise, solve the system using the inverse of a 22 matrix 34. 12x+15y=1412x35y=94 For the following exercise, solve the system using the inverse of a 22 matrix 35. 3x2y+5z=215x+4y=37x2y5z=5 For the following exercise, solve the system using the inverse of a 22 matrix 36. 4x+4y+4z=402x3y+4z=12x+3y+4z=9 For the following exercise, solve the system using the inverse of a 22 matrix 37. 6x5yz=31x+2y+z=63x+3y+2z=13 For the following exercise, solve the system using the inverse of a 22 matrix 38. 6x5y+2z=42x+5yz=122x+5y+z=12 For the following exercise, solve the system using the inverse of a 22 matrix 39. 4x2y+3z=122x+2y9z=336y4z=1 For the following exercise, solve the system using the inverse of a 22 matrix 40. 110x15y+4z=41215x20y+25z=101310x+4y310z=23 For the following exercise, solve the system using the inverse of a 22 matrix 41. 12x15y+15z=3110034x14y+12z=74045x12y+32z=14 For the following exercise, solve the system using the inverse of a 22 matrix 42. 0.1x+0.2y+0.3z=1.40.1x0.2y+0.3z=0.60.4y+0.9z=2 For the following exercise, use a calculator to solve the system equations with matrix inverses. 43. 2xy=3x+2y=2.3 For the following exercise, use a calculator to solve the system equations with matrix inverses. 44. 12x32y=432052x+115y=314 For the following exercise, use a calculator to solve the system equations with matrix inverses. 45. 12.3x2y2.5z=236.9x+7y7.5z=78y5z=10 For the following exercise, use a calculator to solve the system equations with matrix inverses. 46. 0.5x3y+6z=0.80.7x2y=0.060.5x+4y+5z=0 For the following exercises, find the inverse of the given matrix. 47. [1010010101100011]For the following exercises, find the inverse of the given matrix. 48. [1025000202101301]For the following exercises, find the inverse of the given matrix. 49. [1230010214235011]For the following exercises, find the inverse of the given matrix. 50. [1202302100003010200100120]For the following exercises, find the inverse of the given matrix. 51. [100000010000001000000100000010111111]For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 52. 2,400 tickets were sold for a basketball game. If the prices for floor 1 and floor 2 were different, and the total amount of money brought in is $64,000, how much was the price of each ticket?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 53. In the previous exercise, if you were told there were 400 more tickets sold for floor 2 than floor l, how much was the price of each ticket?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 54. A food drive collected two different types of canned goods, green beans and kidney beans. The total number of collected cans was 350 and the total weight of all donated food was 348 1b, 12 oz. If the green bean cans weigh 2 oz less than the kidney bean cans, how many of each can was donated?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 55. Students were asked to bring their favorite fruit to class. 95% of the fruits consisted of banana, apple, and oranges. If oranges were twice as popular as bananas, and apples were 5% less popular than bananas, what are the percentages of each individual fruit?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 56. A sorority held a bake sale to raise money and sold brownies and chocolate chip cookies. They priced the brownies at $l and the chocolate chip cookies at $0.75. They raised $700 and sold 850 items. How many brownies and how many cookies were sold?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 57. A clothing store needs to order new inventory. It has three different types of hats for sale: straw hats, beanies, and cowboy hats. The straw hat is priced at $13.99, the beanie at $7.99, and the cowboy hat at $14.49. If 100 hats were sold this past quarter, $1,119 was taken in by sales, and the amount of beanies sold was 10 more than cowboy hats, how many of each should the clothing store order to replace those already sold?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 58. Anna, Ashley, and Andrea weigh a combined 370 lb. If Andrea weighs 20 1b more than Ashley, and Anna weighs 1.5 times as much as Ashley, how much does each girl weigh?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 59. Three roommates shared a package of 12 ice cream bars, but no one remembers who ate how many. If Tom ate twice as many ice cream bars as Joe, and Albert ate three less than Tom, how many ice cream bars did each roommate eat?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 60. A farmer constructed a chicken coop out of chicken wire, wood, and plywood. The chicken wire cost $2 per square foot, the wood $10 per square foot, and the plywood $5 per square foot. The farmer spent a total of $51, and the total amount of materials used was 14 ft2. He used 3 ft2 more chicken wire than plywood. How much of each material in did the farmer use?For the following exercises, write a system of equations that represents the situation. Then, solve the system using the inverse of a matrix. 61. Jay has lemon, orange, and pomegranate trees in his backyard. An orange weighs 8 oz, a lemon 5 oz. and a pomegranate 11 oz. Jay picked 142 pieces of fruit weighing a total of 70 1b, 10 oz. He picked 15.5 times more oranges than pomegranates. How many of each fruit did Jay pick?Use Cramer's Rule to solve the 22 system of equations. x+2y=112x+y=13 Find the determinant of the 33 matrix. det(A)=|137111123|Use Cramer's Rule to solve the 33 matrix. x3y+7z=13x+y+z=1x2y+3z=4 Explain why we can always evaluate the determinant of a square matrix.Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is O. For simplicity, use a 22 .Explain what it means in terms of an inverse for a matrix to have a 0 determinant.The determinant of 22 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, explain how to find the determinant and provide the answer.For the following exercises, find the determinant. |1234|For the following exercises, find the determinant. |1234|For the following exercises, find the determinant. |2516|

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