1. Find the inverse of the following matrices by the [A[I] → [I|A¯¹] meth a. A A=|-7 -1⁰ 3 -1 - 12/2² -3 L-2 b. A = 1 0 -3]

Q: Let A - = [5 2 0 -2 0-2 7 2 6 = PDPT where D = Compute (a) an orthogonal decomposition A…

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Q: Show that y₁ = ecos(2x) and y2 = e sin(2x) are two linearly independent solutions of d'y dy dz² +2-…

A: We have to show that  and  are two linearly independent solution of the differential equation

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Q: A company wants to lay cable across a lake. To find the length of the lake, they made the following…

A: Suppose that the  length of the  lake  is  ftFrom the  given figure suppose  that  the  given…

Q: 2. The behavior of the system is a saddle. x' = − x+y, |y' = − x − y -

A: (.) Given system is,                   We write the given system in matrix form,

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Q: Problem 1 Determine which of the following bases are orthogonal, and then determine which are…

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Q: I understood that just fine, but what is stumping me is how to show that there is a limit using…

A: We shall show that the limit exists using the above theorem.

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Q: Prove that the dual of (P1) has a finite optimal valı

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Q: 6. Solve the Cauchy problem Ut + xux = -tu, u(x,0) = = COS I.

A: According to the Bartleby guidelines I have solved one question.For remaining questions you can…

Q: 1. Region D of the (x, y)-plane is the locus of points satisfying the conditions 2y > e-¤ > y and y…

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Q: A basis for the null space of the Matrix 1 2 3 A 2 4 6 is - 1 a. O b. O C. 00 { { { - 3 0 |} 1 2 0 1…

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Q: Identify the equation of the quadratic function with a vertex of (0, -1), that passes through the…

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Q: Let V = (x)i + (5y)j + (2z)k be a vector field. Let St the upward-oriented surface given by z = 4x²…

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Q: Find all semistationary solutions of the following system of differential equations. dy dt dx dt = x…

A: To find the semi-stationary solutions of the given system of differential equations, we'll first set…

Q: Vector field F is given by F(r) = (x, y, z + 1) and surface A is the locus of points satisfying z +…

A: The given vector field is .The given surface  is the locus of points satisfying  for .We need to…

Q: Find the eigenvalues making sure that each 20 = Yn(x) = and eigenfunctions yn(x) for the given…

A: Here c1,c2 are arbitrary constants.

Q: 13. Two airplanes depart from the same place at 2:00 p.m. One plane flies south at speed of 376…

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Q: Second Order Diff Eqns: Use the Cauchy-Euler Equations to solve the Initial Value Problem where…

A: The differential equation of the following form is called the Cauchy-Euler equation:It is given that…

Q: The system of first order differential equations: ไม่ โ = = -8 y₁+ 2 y2, 52 1 + 12 32, 31 (0) = −4…

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Q: ints A-F in the figure. 100 M M 19 04 T NO | સ A 0= JU 4 0= 1 2 3 4 5 E 6 X Select all that apply.…

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Q: prove that | Sinsy | dy лу ∞

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Q: To minimize th Radius of the c Height of the c Minimum cost:

A: We want to minimize  costs. Note that we have the constraint that it must hold 250 cubic centimeters…

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A: The objective of the question is to translate the given statements into symbolic form and choose the…

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A: Given information:Data on corn yield (bushels per acre) and total production (million bushels) for…

Q: Shot that f(x) = x^2+ x - 3 has a solution in the interval [0,2]. Determine the number of iterations…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [az]. How many valid…

A: We shall count this using basic mathematics.

Q: Cross product is a linear transformation from R³ →R³ You can define it as X1 X2 X3 X Y1 Y2 Y3 = det(…

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Q: 5. Let f RR be a uniformly continuous function. Show that there are constants : A, B such that…

A: Let   be  a  uniformly  continuous  function  on We  have  to show  that  there  exists  positive…

Q: Valencia Products makes automobile radar detectors and assembles two models: LaserStop and…

A: Objective function:Maximum profit: Subjected to constraints:where L is the number of LaserStop…

Q: 1 -1 1 -1 1 -2 0 (a) does the inverse of the matrix exist? Your answer is (input Yes or No): Yes (b)…

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Q: Let a₁ [4] 9 āz DNE Is b a linear combination of a₁ and a2? and Ob is not a linaer combination of a₁…

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Q: Let A = {x + iy : x 0}. Determine the set of all z for which A. (Hint: this is {z : Re() 0}. Find…

A: Set of Z found.

Q: Suppose F(x, y) = (4x - 3y)i + 2xj and C is the counter-clockwise oriented sector of a circle…

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Q: Construct the 5th term in sequence based on recursive definition. Show how you derive each term…

A: Construct the 5th term in sequence based on recursive definition. Show how you derive each term…

Q: Suppose ƒ and g are continuous at a. Prove the following using e-d arguments. (a) fg is continuous…

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Q: The figure below shows the derivative F' of F. Let F (0) = 0. F(x) लिए 4 1 2 3 of the four numbers F…

A: GivenThe graph of the derivative of the function is given in the question and also the function…

Q: a. Sketch the region of integration, D, for which y=√x (4x+10y) dA= (4x+10y) dy dx. y=? 2-0 y=z b.…

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Q: Follow the steps for graphing a rational function to graph the function F(x)= x² +7x-8 x+2 OC. The…

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Q: Find the volume of the upper region cut from the solid sphere rho <= 1 by the cone phi = pi / 3

A: We have to find the volume of the upper region cut from the solid sphere ρ≤ 1 by the cone  ϕ= π3

Q: 4. Let S be a sphere of radius r and P a point inside or outside the sphere. Show that 1 √√₂₁ P |dx|…

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Q: Consider the vector space V over the real numbers, consisting of all polynomials of degree less than…

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Q: J cos(y + x) dA, Problem 6. Use a change of variables to evaluate where P is the parallelogram…

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Q: Let A be a diagonalisable 3 x 3 matrix with rational entries. Working over R on V = R³: (a) Is it…

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A: The problem can be solved using trigonometry and given information. Let's denote the height of the…

Q: In each of Problems 12 through 15, use integration by parts to find the Laplace transform of the…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 35 40 i The small ants first destroy the large ant colony in year The large ants harvest the fruit…

A: (a) We have to Construct a table showing each colony's population in years t = 5, 10, 15, 20, 25,…

Q: Let 7= X1 Describe all solutions of a₁₁ + a₂2 +33 + 44 = Ō. I2 X3 C4 18 = x2 13 ā₂ - [3]₁03 = [27],…

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Q: 2. Let u₁ -8 ] 10 4 Determine if x is in the span of ₁, ₂, and 3. If x is in the span then express…

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