. Matrices A and B are said to be similar if and only if there is a matrix P such that A = PBP^-1 . If A and B are similar, show that 1) Det A = det B 2) A and B together have an inverse or do not have an inverse. 3) The characteristic equations of A and B are the same.

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Q: Suppose A and B have the same eigenvalues A₁,..., An with the same independent eigenvectors ₁,...,n.…

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Q: Matrices A and B are said to be similar if and only if there is a matrix P such that A = PBP^-1 . If…

A: This question is related to topic similar matrix

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Q: b) 3 -2 Given matrix A = -2 6 2. Suppose the eigenvalues of A and the bases for the 4 2…

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Q: The set of eigenvalues of the matrix A=[2 0 -1; 6 8 -5; 9 9 -7]∈ R^3x3is equal to: (a) {1,2}, (b)…

A: Step 1: The provided matrix is:A=⎣⎢⎡​269​089​−1−5−7​⎦⎥⎤​∈R3×3   .........(1)It is needed to…

Q: A 1 6 -3 -5 a) The eigenvalues of A are and

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Q: Q6. Find eigenvalues and associated eigenvectors for each matrix. [-1 4 -1] b) A = 0 1 0 03-21 a) A…

A: Given  A = 8-63-1                      The characteristic equation of A is…

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Q: Find a 2 x 2 matrix A that has eigenvalues X₁ = 6 and X₂=5 and corresponding eigenvectors: 1 (2)…

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Q: 35. Give an example of a 4 x 4 matrix A without real eigen- values. ANS: Го -1 07 1 A = 0 0 -1 0 1

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Q: 4 1 Let A = then the eigenvalues of A are: 1 4 Select one: а. 5,5 b. 3,-3 с. 5,0 d. 3,5

A: Given matrix: