Let A be an n × n matrix and let r be any constant and k a positive integer. Find a formula for the following and justify your answer (show all your work). (a) det(rA), (b) det(Ak

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Q: Let A be an n xn matrix and let r be any constant and ka positive integer. Find a formula for the…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 A = - 4 -3 L = U =

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A: Solution Given A=3421We need to find the product of elementary matrices

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Q: Let A be an n x n matrix and let r be any constant and k a positive integer. Find a formula for the…

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Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

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Q: Give an example of  a matrix which is its own inverse ( that is , where A−1=AA−1=A)

A: To give the example of the matrix whose inverse is matrix it sef. That is: A-1=A

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Q: Let A be an n x n matrix and let r be any constant and k a positive integer. Find a formula for the…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). -2 0 4 A= 4 3 -3 4 18 30 L…

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Q: Determine whether th e given matrix is orthogonal. If it is, find its inverse

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Q: 5. Consider the 3 × 2 matrix A such that 3 A and A 5 3 (a) Write down A. (b) Is A singular? Justify…

A: For the given information, we have to answer the following...

Q: Find x such that the matrix is singular. [ х 7 A = -5 2 X =

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Q: Find x such that the matrix is singular. [ х 3 A = -9 8 X =

A: The given matrix is: A=x3-98

Q: 6. Find a matrix X such that the equation AX = B holds, where A = 4 and 3. В - 1 8

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Q: +i) is unitary and find A. Prove that the matrix A =

A: Given: A = 121+i12-1+i121+i121-i To do: Prove that A is unitary. Find A-1.

Q: det(cA) = c det(A) Insert a number to sho

A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

Q: Find an invertible matrix X and a diagonal matrix D such that X-1 AX = D. You don't need to compute…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

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Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

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Q: 3 Given that matrix A = (, and matrix B = 1. From the matrix above, 3 Determine the values of x and…

A: The given matrices A=35-10 and B=x0y1

Q: 2. Given the matrix A below, Solve for IAI-¹ A = 1 2 2 1 -1 3 4 6 3 5 2 -3 -3 8 7 4.

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Q: Let A be an n x k matrix, for some positive integers n and k . Suppose we are given that rank(A) #0,…

A: Let A be an n×k matrix, for some positive integers n and k.  We have given,  rank(A) ≠ 0 with…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). -5 0 4 A = 15 2 - 9 15 8 8…

A: Given that  The matrix A  To find the LU by using LU factorization

Q: Solve for the matrix X if AX = B. Assume that all matrices are n X n and invertible as needed.

A: Given that, AX=B Assume that A is of order n×n such that A is invertible. Hence, A-1 exist. Since,…

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Q: ue? 0 0.

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Q: Let A be an n x n matrix and let r be any constant and k a positive integer. Find a formula for the…

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Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: 2. Find the inverse matrix for A=|

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: The idea of elementary matrices are  En•En-1•....... •E1•A=I So we need to find matrices E

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 A = - 4 3 L = U =

A: Given that, A = LU

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Q: Find the value of k that makes the matrix singular.   4k + 1 3   −9 1 k =

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Q: Find the inverse of the matrix. For what value(s) of x, if any, does the matrix have no inverse?

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A: Given: A=-6669-8-12-334 To find the invertible matrix A as a product of elementary matrix.

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Q: If A is an n × n matrix, what are the entries on the main diagonal of A − AT ? Justify your answer.

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Q: Let a - .- 3 -1 21 A = [ 1.8 = ; -21 -31

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