Let A be an n×n matrix with n different positive eigenvalues. Prove that there exists a matrix B such that B2 = A. Is B uniquely determined? Please do this step by step in detail, show why you are allowed to take certain steps, I often have problems finding the right theorem to apply.

Q: 7. Give an example of each matrix of order 3x3 which has three values of different eigenvalues, two…

A: We want to consider a 3×3 matrix.

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Q: For the linear system j' Find the eigenvalues and eigenvectors for the coefficient matrix. , 01 = ,…

A: See solution below

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Q: EXAMPLE 6 We can use Gaussian elimination to find a right inverse of an m xn matrix A, so long as…

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Q: 3.2 Exercises PS2.9 Consider the matrices: A = (a) -2A (b) B-2A 0 -5 -1 -5 B-4 0-1 C= = Compute each…

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Q: Assume all matrices are invertible. Solve for X: A(XB – D) = B

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Q: 11. Consider the vector space generated by [1, 1,1, 1), [1, 1, 2, 4), (1,2, -4, –3). Find an…

A: Note: according to our guidelines we can answer only 11 th question

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Q: Given the 2 by 2 matrix A, find the eigenvalues and eigenvectors by hand, and if possible, the…

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Q: Matrix A is invertible matrix and has the dimensions 3 x 3 Determine the rank of A and dimension of…

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Q: (a) The matriz 1 3 -1 0 5 3 0 2 is invertible. Find A- by any method you know.

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Q: 3. Find all the Eigenvalues and Eigenvectors of the following matrix. Then diagonalize the matrix by…

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Q: 3. 4. Consider the matrix -2 4. (a) Find the eigenvalues of A. (b) Find two eigenvectors v and w of…

A: According to our guidelines we are supposed to answer only first three subparts.kindly repost other…

Q: Find the inverse of the matrix 2 A= 2 -3-3 -31

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Q: Find the QR factorization of the matrix   Please show all work

A: The given problem is to find the qr factorization for the given matrix. Given matrix [0 1 1 ; 1 0 1…

Q: Let A = 52 (b) Find lim A". n→∞ | 312 716 9 4 54 (a) Find a matrix B so that B² = A.

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Q: If the diagonal matrix that is congruent to the given matrix is  2 0 0 0 -1 0 0 0 0 Can we…

A: Given matrix is A=−101011011. And the diagonal matrix that is congruent to the given matrix A is…

Q: Let A be a 5 x 3 matrix and assume that N(A) is trivial, i.e.. N(A) = {0}. Find dim C(A).

A: Given that A be a 5*3 matrix. and N(A)={0}. we have to find the dim C(A)?

Q: If A is an orthogonal matrix, then it has a dominant eigenvalue. True O False

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Q: |1/2 A = 2 -3 1. Find sequence of elementary matrices whose product is 3/15

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Q: 3. Find a basis among the vectors [1, 2, 3], [2, 6, 10], [0, –3, –6],[-1,-3,-5] (which are surely…

A: Q3 asked and answered.

Q: 2. Compute the inverse of the Hadamard matrix 1 1 1 -1 -1 -1 -1 1 -1 1-1 H 1

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Q: lease explain how I would find the eigenvectors of the matrix in the picture. I know that the…

A: The matrix given is

Q: Find the inverse of the matrix 2 2 2 -3 -3 !

A: Given  A = 122112-3-31

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Suppose that the matrix -37 A I has eigenvector V = Determine the value of z. Enter your answer…

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Q: 2. Find fundamental (3 (a) x' = (b) x' = 2-5 4 matrices for the following systems: :)> (9) -2 62 5 3…

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