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All Textbook Solutions for Precalculus

Explain the meaning of the notation 3R1+R2R2.Explain the meaning of the notation 4R2+R3R3.For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) 3x+2yz=48x+4z=122y5z=1 For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) 4xy+z=82x+5z=11y7z=6 For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) 4x2y=6y+23x=5y+7 For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) 2yx=48x5y=6x For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) x=2y=67z=12 For Exercises 9-14, write the augmented matrix for the given system. (See Example 1) x=4y=2z=12 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 4611391 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 372114 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 1438012120016 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 112401380012 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 1008010900132 For Exercises 15-20, write a system of linear equations represented by the augmented matrix. (See Example 1) 1002010600112 For Exercises 21-26, perform the elementary row operations on 142366. (See Example 2) R1R2 For Exercises 21-26, perform the elementary row operations on 142366. (See Example 2) 13R2R2 For Exercises 21-26, perform the elementary row operations on 142366. (See Example 2) 3R1R1 For Exercises 21-26, perform the elementary row operations on 142366 . (See Example 2) 3R1R1 For Exercises 21-26, perform the elementary row operations on 142366 . (See Example 2) 13R2+R1R1 For Exercises 21-26, perform the elementary row operations on 142366 . (See Example 2) 3R1+R2R2 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) R2R3 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) R1R2 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) 14R3R3 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) 12R2R2 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) 2R1+R2R2 For Exercises 27-32, perform the elementary row operations on 1562215142310 . (See Example 2) 4R1+R3R3 For Exercises 33-36, determine if the matrix is in row-echelon form. If not, explain why. 154026 For Exercises 33-36, determine if the matrix is in row-echelon form. If not, explain why. 164201010313 For Exercises 33-36, determine if the matrix is in row-echelon form. If not, explain why. 132601590000 For Exercises 33-36, determine if the matrix is in row-echelon form. If not, explain why. 142601320010 For Exercises 37-40, determine if the matrix is in reduced row-echelon form. If not, explain why. 100310041005 For Exercises 37-40, determine if the matrix is in reduced row-echelon form. If not, explain why. 102301040015 For Exercises 37-40, determine if the matrix is in reduced row-echelon form. If not, explain why. 10001010020010700014 40PE For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) 2x+3y=13x+4y=14 42PE 43PE 44PE 45PE 46PE 47PE 48PE 49PE 50PE 51PE For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) 2x+5y4z=4x2y+z=3x5y+9z=5 For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) 2x+8z=7y46x=3y3z186z=5yx34 For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) 2x=7y3zx+y=z+516z=2yx4 55PE 56PE 57PE 58PE For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) x1+x2+5x4=4x2+2x4=32x2+x33x4=53x1+3x2+17x4=10 For Exercises 41-60, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Examples 3-5) x1+x35x4=12x1+x22x3+16x4=3x1+2x310x4=5x1x3+7x4=7 For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Andre borrowed $20,000 to buy a truck for his business. He borrowed from his parents who charge him 2 simple interest. He borrowed from a credit union that charges 4 simple interest, and he borrowed from a bank that charges 5 simple interest. He borrowed five times as much from his parents as from the bank, and the amount of interest he paid at the end of 1yr was $620. How much did he borrow from each source?For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Sylvia invested a total of $40,000 . She invested part of the money in a certificate of deposit (CD) that earns 2 simple interest per year. She invested in a stock that returns the equivalent of 8 simple interest, and she invested in a bond fund that returns 5 . She invested twice as much in the stock as she did in the CD, and earned a total of $2300 at the end of 1yr . How much principal did she put in each investment?For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Danielle stayed in three different cities (Washington, D.C., Atlanta, Georgia, and Dallas, Texas) for a total of 14 nights. She spent twice as many nights in Dallas as she did in Washington. The total cost for 14 nights (excluding tax) was $2200 . Determine the number of nights that she spent in each city.For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Three pumps (A , B , and C ) work to drain water from a retention pond. Working together the pumps can pump 1500gal/hr of water. Pump C works at a rate of 100gal/hr faster than pump B . In 3hr , pump C can pump as much water as pumps A and B working together in 2hr . Find the rate at which each pump works.For Exercises 65-66, find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A , B , and C. 5x26x13x+3x22=Ax+3+Bx2+Cx22 For Exercises 65-66, find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian elimination to find A , B , and C . 2x2+17x+3x+5x+12=Ax+5+Bx+1+Cx+12 Explain why interchanging two rows of an augmented matrix results in an augmented matrix that represents an equivalent system of equations.Explain why multiplying a row of an augmented matrix by a nonzero constant results in an augmented matrix that represents an equivalent system of equations.Explain the difference between a matrix in row-echelon form and reduced row-echelon form.Consider the matrix 59571212. Identify two row operations that could be used to obtain a leading entry of 1 in the first row. Also indicate which operation would be less cumbersome as a first step toward writing the matrix in reduced row-echelon form.71PE For Exercises 71-72, use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x,y , and z are rounded to 2 decimal places. 3.61x+8.17y5.62z=30.28.04x3.16y+9.18z=28.40.16+0.09y+0.55z=4.6 A small grocer finds that the monthly sales y (in $ ) can be approximated as a function of the amount spent advertising on the radio x1 (in $ ) and the amount spent advertising in the newspaper x2 (in $ ) according to y=ax1+bx2+c . The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months. a. Use the data to write a system of linear equations to solve for a,b , and c . b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y=ax1+bx2+c . d. Predict the monthly sales if the grocer spends $2500 advertising on the radio and $500 advertising in the newspaper for a given month.The purchase price of a home y (in $1000 ) can be approximated based on the annual income of the buyer x1 (in $1000 ) and on the square footage of the home x2 (in 100ft2 ) according to y=ax1+bx2+c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a. Use the data to write a system of linear equations to solve for a,b , and c . b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y=ax1+bx2+c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500ft2 home.For Exercises 75-76, the given function values satisfy a function defined by fx=ax2+bx+c. a. Set up a system of equations to solve for a , b , and c . b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write a function of the form fx=ax2+bx+c that fits the data. f3=7.28f1=3.68f10=18.2 For Exercises 75-76, the given function values satisfy a function defined by fx=ax2+bx+c a. Set up a system of equations to solve for a , b , and c . b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write a function of the form fx=ax2+bx+c that fits the data. f3=6.95f2=20.2f12=39.8 Solve the system 5x9y33z=3x2y7z=02x+y+8z=12 Solve the system. 0.3x0.1y=2y20=3x Solve the system. 4x11y+3z=24x+3yz=73x+11y5z=29 Solve the system. x3y17z=172x+7y+38z=40 Solve the system. 2x3y+5z=34x6y+10z=620x30y+50z=30 Refer to the figure. Assume that traffic flows freely with flow rates given in vehicles per hour. a. If the traffic between intersections D and A is 400 vehicles per hour, determine the flow rates x1,x2 , and x3 . b. If the traffic between intersections D and A is between 380 and 420 vehicles per hour, determine the flow rates x1,x2 , and x3 .True or false? A system of linear equations in three variables may have no solution.True or false? A system of linear equations in three variables may have exactly one solution.True or false? A system of linear equations in three variables may have exactly two solution.True or false? A system of linear equations in three variables may have infinitely many solutions.If a system of linear equations has no solution, then the system is said to be .If a system of linear equations has infinitely many solutions, then the equations are said to be .For Exercises 7-14, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 124005 For Exercises 7-14, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 102501420001 For Exercises 7-14, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 104301160000 10PE For Exercises 7-14, an augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 100301040010 12PE 13PE 14PE For Exercises 15-18, determine the solution set for the system represented by each augmented matrix. a. 125010 b. 125000 c. 125001 16PE 17PE 18PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 2x+4y=5x+2y=4 20PE 21PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 4x3y=6y=43x2 23PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) x3y+17z=1xy+7z=22x5y+29z=5 25PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) x+3y+9z=122x+7y+22z=265x17y53z=64 For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 2x=5y16z+402x+y=4zx2y+7z=18 28PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 2x5y20z=24x3y11z=15 For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 2xy5z=3x2y7z=12 For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 2x+3y+4z=124x6y8z=24x+1.5y+2z=6 32PE 33PE 34PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) 5x+12y20z=11x+4z=3y+1 36PE For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) x13x2+9x314x4=32x23x3+6x4=10x2x3+2x4=4x12x2+8x312x4=24 For Exercises 19-38, solve the system by using Gaussian elimination or Gauss-Jordan elimination. (See Exercises 1-5) x13x312x4=15x2+x3+6x4=8x22x36x4=72x1+4x3+16x4=22 39PE 40PE For Exercises 41-44, the solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. Answers may vary. 4z,6z,zzisanyrealnumber 42PE 43PE For Exercises 41-44, the solution set to a system of dependent equations is given. Write three ordered triples that are solutions to the system. Answers may vary. 4y+2z20,y,zyandzisanyrealnumber For Exercises 45-48, assume that traffic flows freely through the intersections A,B,C , and D . The values x1,x2,x3 , and x4 and the other numbers in the figures represent flow rates in vehicles per hour.(See Example 6) a. Write an equation representing equal flow into and out of intersection A . b. Write an equation representing equal flow into and out of intersection B . c. Write an equation representing equal flow into and out of intersection C d. Write the system of equations from parts (a)-(c) in standard form. e. Write the reduced row-echelon form of the augmented matrix representing the system of equations from part (d). f. If the flow rate between intersections A and C is 120 vehicles per hour, determine the flow rates x1 and x2 . g. If the flow rate between intersections A and C is between 100 and 150 vehicles per hour, inclusive, determine the flow rates x1 , and x2 .46PE 47PE 48PE An accountant checks the reported earnings for a theater for three nightly performances against the number of tickets sold. a. Let x,y , and z represent the cost for children tickets, student tickets, and general admission tickets, respectively. Set up a system of equations to solve for x,y , and z . b. Set up the augmented matrix for the system and solve the system. (Hint. To make the augmented matrix simpler to work with, consider dividing each linear equation by an appropriate constant) c. Explain why the auditor knows that there was an error in the record keeping.A concession stand at a city park sells hamburgers, hot dogs, and drinks. Three patrons buy the following food and drink combinations for the following prices. a. Let x,y , and z represent the cost for a hamburger, a hot dog, and a drink, respectively. Set up a system of equations to solve for x,y , and z . b. Set up the augmented matrix for the system and solve the system. c. Explain why the concession stand manager knows that there was an error in the record keeping.51PE 52PE 53PE The systems in Exercises 53-56 are called homogeneous systems because each has 0,0,0 as a solution. However, if a system is made up of dependent equations, it will have infinitely many more solutions. For each system, determine whether 0,0,0 is the only solution or if the system has infinitely many solutions. If the system has infinitely many solutions, give the solution set. x2y7z=03x+8y+31z=02x+5y+22z=0 55PE 56PE 57PE 58PE Consider the following system. By inspection describe the geometrical relationship among the planes represented by the three equations. x+y+z=12x+2y+2z=23x+3y+3z=3 Explain why a system of two equations with three variables cannot have exactly one ordered triple as its solution.For Exercises 61-66, use a graphing utility to find the reduced row-echelon form of the augmented matrix for the system in the given exercise. Use the result to verify the answer to the given exercise Exercise 23 For Exercises 61-66, use a graphing utility to find the reduced row-echelon form of the augmented matrix for the system in the given exercise. Use the result to verify the answer to the given exercise Exercise 24 63PE For Exercises 61-66, use a graphing utility to find the reduced row-echelon form of the augmented matrix for the system in the given exercise. Use the result to verify the answer to the given exercise Exercise 26 For Exercises 61-66, use a graphing utility to find the reduced row-echelon form of the augmented matrix for the system in the given exercise. Use the result to verify the answer to the given exercise Exercise 31 For Exercises 61-66, use a graphing utility to find the reduced row-echelon form of the augmented matrix for the system in the given exercise. Use the result to verify the answer to the given exercise. Exercise 32 Determine the order of each matrix. a. 924.1334 b. 411 c. 0.10.40.50.2 d. 105311 2SP 3SP 4SP Given A=43111 and B=2165 , solve 2X+A=B for X .6SP 7SP A farmer sells organic zucchini, yellow squash, and corn in two different roadside stands. Matrix Q represents the number of pounds of each type of vegetable sold at each stand. Matrix P gives the price per pound of each item. Find the product QP and interpret the result. YellowZucchinisquashCornQ=424084303690Stand1Stand2 P=$4.00$3.40$4.20ZucchiniYellowsquashCorn Use matrix A from Example 9. Find the product 1001 . A and determine the effect on the graph of the triangle in Figure 9-6.If the of a matrix is pq , then p represents the number of and q represents the number of .A matrix with the same number of rows and columns is called a matrix.What are the requirements for two matrices to be equal?An mn matrix whose elements are all zero is called a matrix.To multiply two matrices A and B , the number of of A must equal the number of of B .If A is a 53 matrix and B is a 37 matrix, then the product AB will be a matrix of order . The product BA (is/is not) defined.True or false: Matrix multiplication is a commutative operation.True or false: If a row matrix A and a column matrix B have the same number of elements of elements, then the product AB is defined.What is a row matrix?What is a column matrix?For Exercises 11-16, a. Give the order of the matrix. b. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. (See Example 1) 3511231.7 For Exercises 11-16, a. Give the order of the matrix. b. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. (See Example 1) 15621323016.112 For Exercises 11-16, a. Give the order of the matrix. b. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. (See Example 1) 317 For Exercises 11-16, a. Give the order of the matrix. b. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. (See Example 1) 2.46.9 For Exercises 11-16, a. Give the order of the matrix. b. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. (See Example 1) 4284 16PE 17PE For Exercises 17-22, determine the value of the given element of matrix A=aij .(See Example 2) A=36132405118.61242 a32 19PE 20PE For Exercises 17-22, determine the value of the given element of matrix A=aij .(See Example 2) A=36132405118.61242 a43 22PE 23PE 24PE 25PE Given C=1639 , find the additive inverse of C .27PE 28PE For Exercises 27-32, add or subtract the given matrices if possible. (See Example 3) A=6172122B=926.22138C=11411316D=2381616 CA+B 30PE 31PE For Exercises 27-32, add or subtract the given matrices if possible. (See Example 3) A=6172122B=926.22138C=11411316D=2381616 C+D 33PE Given matrix A , explain how to find its additive inverse A .For Exercises 35-42, use A=2491312 and B=1042923 . (See Example 4) 3A 36PE For Exercises 35-42, use A=2491312 and B=1042923 . (See Example 4) 2A7B 38PE 39PE 40PE For Exercises 35-42, use A=2491312 and B=1042923 . (See Example 4) 3A+5AB 42PE 43PE For Exercises 43-48, use A=1642 and B=2469 and solve for X . (See Example 5) 3X+A=B For Exercises 43-48, use A=1642 and B=2469 and solve for X . (See Example 5) A+5X=B For Exercises 43-48, use A=1642 and B=2469 and solve for X . (See Example 5) B4X=A For Exercises 43-48, use A=1642 and B=2469 and solve for X . (See Example 5) 2AB=10X For Exercises 43-48, use A=1642 and B=2469 and solve for X . (See Example 5) 3BA=2X 49PE 50PE 51PE 52PE For Exercises 53-64, (See Examples 6-7) a. Find AB if possible. b. Find BA if possible. c. Find A2 if possible. A=2357andB=1413 54PE 55PE 56PE For Exercises 53-64, (See Examples 6-7) a. Find AB if possible. b. Find BA if possible. c. Find A2 if possible. A=923154017andB=150 58PE 59PE For Exercises 53-64, (See Examples 6-7) a. Find AB if possible. b. Find BA if possible. c. Find A2 if possible. A=4341andB=51213 61PE 62PE 63PE For Exercises 53-64, (See Examples 6-7) a. Find AB if possible. b. Find BA if possible. c. Find A2 if possible. A=6andB=2 65PE 66PE For Exercises 65-68, find AB and BA . A=100010001andB=95365122301 68PE Matrix D gives the dealer invoice prices for sedan and hatchback models of a car with manual transmission or automatic transmission. Matrix M gives the MSRP (manufacturer's suggested retail price) for the cars. SedanHatchbackD=$29,000$27,500$28,500$26,900ManualAutomatic SedanHatchbackM=$32,600$29,900$31,900$28,900ManualAutomatic a. Compute MD and interpret the result. b. A buyer thinks that a fair price is 6 above dealer invoice. Use scalar multiplication to determine a matrix F that gives the fair price for these cars for each type of transmission.In matrix C , a coffee shop records the cost to produce a cup of standard Columbian coffee and the cost to produce a cup of hot chocolate. Matrix P contains the selling prices to the customer. CoffeeChocolateC=$0.90$0.84$1.26$1.151.641.50SmallMediumLarge CoffeeChocolateP=$3.05$2.25$3.65$3.05$4.15$3.65SmallMediumLarge a. Compute PC and interpret its meaning. b. If the tax rate in a certain city is 7 , use scalar multiplication to find a matrix F that gives the final price to the customer (including sales tax) for both beverages for each size. Round each entry to the nearest cent.71PE 72PE An electronics store sells three models of tablets. The number of each model sold during "Black Friday" weekend is given in matrix A . The selling price and profit for each model are given in matrix B . (See Example 8) ModelABCA=847032624816704012FridaySaturdaySunday SellingPriceProfitB=$499$200$599$240$629$280ABModelC a. Compute AB and interpret the result. b. Determine the total revenue for Sunday. c. Determine the total profit for the 3 -day period for these three models.74PE The labor costs per hour for an electrician, plumber, and air-conditioning/heating expert are given in matrix L . The time required from each specialist for three new model homes is given in matrix T . Cost/hrL=$45$38$35ElectricianPlumberAC/heating Time(hr)ElectricianPlumberAC/heatingT=22161428211818149Model1Model2Model3 a. Which product LT or TL gives the total cost for these three services for each model? b. Find a matrix that gives the total cost for these three services for each model.The number of calories burned per hour for three activities is given in matrix N for a 140-lb woman training for a triathlon. The time spent on each activity for two different training days is given in matrix T . Calories/hrN=540400360RunningBicyclingSwimming TimeRunningBicyclingSwimmingT=45min1hr30min1hr1hr30min45minDay1Day2 a. Which product NT or TN gives the total number of calories burned from these activities for each day? b. Find a matrix that gives the total number of calories burned from these activities for each day.77PE 78PE 79PE 80PE a. Write a matrix A that represents the coordinates of the vertices of the quadrilateral. b. What operation on A will shift the graph of the quadrilateral 3 units downward? c. What operation on A will shift the graph 4 units to the left? d. Use matrix multiplication to reflect the graph across the x-axis. e. Use matrix multiplication to reflect the graph across the y-axis.a. Write a matrix A that represents the coordinates of the vertices of the quadrilateral. b. What operation on A will shift the graph of the quadrilateral 6 units downward? c. What operation on A will shift the graph 2 units to the left? d. Use matrix multiplication to reflect the graph across the x-axis. e. Use matrix multiplication to reflect the graph across the y-axis.83PE 84PE For Exercises 85-86, use the following gray scale. a. Write a 53 matrix that represents the letter E in dark gray a white background. b. Use matrix addition to change the pixels so that the letter E is medium dark on a light gray background.86PE 87PE For Exercises 87-92, use matrices A,B , and C to prove the given properties. Assume that the elements within A,B , and C are real numbers. A=a1a2a3a4B=b1b2b3b4C=c1c2c3c4 Associate property of matrix addition A+B+C=A+B+C 89PE For Exercises 87-92, use matrices A,B , and C to prove the given properties. Assume that the elements within A,B , and C are real numbers. A=a1a2a3a4B=b1b2b3b4C=c1c2c3c4 Identity property of matrix addition A+0=A For Exercises 87-92, use matrices A,B , and C to prove the given properties. Assume that the elements within A,B , and C are real numbers. A=a1a2a3a4B=b1b2b3b4C=c1c2c3c4 Associative property of scalar multiplication stA=stA For Exercises 87-92, use matrices A,B , and C to prove the given properties. Assume that the elements within A,B , and C are real numbers. A=a1a2a3a4B=b1b2b3b4C=c1c2c3c4 Associative property of scalar multiplication tA+B=tA+tB Given A=i00i , find A2,A3 , and A4 . Discuss the similarities between An and in , where n is a positive integer.94PE 95PE Find the product. aabb1111 97PE 98PE 99PE Given two matrices A and B , how can you determine the order of AB , assuming that the product is defined?For Exercises 101-104, refer to matrices A,B , and C and perform the indicated operations on a calculator A=1.053.94.129.42.41.5 B=10302436188 C=6.24.9 2.5A3.6B For Exercises 101-104, refer to matrices A,B , and C and perform the indicated operations on a calculator A=1.053.94.129.42.41.5 B=10302436188 C=6.24.9 6.4A+B For Exercises 101-104, refer to matrices A,B , and C and perform the indicated operations on a calculator A=1.053.94.129.42.41.5 B=10302436188 C=6.24.9 3AC For Exercises 101-104, refer to matrices A,B , and C and perform the indicated operations on a calculator A=1.053.94.129.42.41.5 B=10302436188 C=6.24.9 7.5BC Given A=34210 show that a. Al2=A b. l2A=A 2SP 3SP Given A=24141310396 find A1 if possible.5SP 6SP Use the inverse of the coefficient matrix found in Skill Practice 4 to solve the system. 2x+4y+z=04x13y+10z=243x9y+6z=15 The symbol ln represents the matrix of order n .In is an nn matrix with â€™s along the main diagonal and â€™s elsewhere.Given an nn matrix A , if there exists a matrix A1 such that AA1=ln and A1A=ln , then A1 is called the of .A .A matrix that does not have an inverse is called a matrix. A matrix that does have an inverse is said to be invertible or Let A=abcd be an invertible matrix. Then a formula for the inverse A1 is given by .Suppose that the matrix equation AX=B represents a system of n linear equations in n variables with a unique solution. Then X= .Write the matrix l2.Write the matrix l3.For Exercises 9-12, verify that a. Aln=A b. lnA=A (See Example 1) A=7855.18 For Exercises 9-12, verify that a. Aln=A b. lnA=A (See Example 1) A=314 For Exercises 9-12, verify that a. Aln=A b. lnA=A (See Example 1) A=1349531164 For Exercises 9-12, verify that a. Aln=A b. lnA=A (See Example 1) A=391041503 For Exercises 13-18, determine whether A and B are inverses. (See Example 2) A=10342andB=14381254 For Exercises 13-18, determine whether A and B are inverses. (See Example 2) A=4186andB=381161214 For Exercises 13-18, determine whether A and B are inverses. (See Example 2) A=231331241andB=110101623 16PE For Exercises 13-18, determine whether A and B are inverses. (See Example 2) A=2134andB=4376 18PE For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=4365 For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=53107 For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=82105 22PE For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=37614 24PE 25PE For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=111112101 27PE 28PE 29PE For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=139272251753 31PE 32PE For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=1250012001102171 For Exercises 19-34, determine the inverse of the given matrix if possible. Otherwise, state that the matrix is singular. (See Examples 3-6) A=1303010224120110 35PE For Exercises 35-38, write the system of equations as a matrix equation of the form AX=B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. 6xy=12x+3y=13 37PE 38PE

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