QUESTION I Consider the operator R³ → R³ given by left-multiplication by the matrix: -6 -8 A = 2 -1 4 -1 6 Find the characteristic polynomial CA(x), the eigenvalues of A, and the eigenspaces of A. What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonaliz- able?

Q: Let A = [a = [a b]. Find a formula for for the eigenvalues of A in terms of a, b, c and d.

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Q: Let A be a 3 x 3 matrix with eigenvalues 7/2, 7//4, 7/8. If the eigenvalues of A- are A1,2, 13, then…

A: we have given eigen values of matrix A these are 7/2,7/4,/7/8 As we know eigen value of A-1 =1/lemda…

Q: 8. Compute the characteristic polynomial of A, the eigenvalues of A, and the basis for each…

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Q: Let A be the matrir A = -6 2 Find the characteristic polynomial and eigenvalues of A.

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Q: Find the characteristic polynomial and the eigenvalues of the matrix : State the multiplicity of…

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Q: Find eigenvectors for each eigenvalue (-3,4) of A: 2x2 matrix below 3 2 3 -2

A: Given, A=323-2

Q: A = (; ) 5 -6 3 -4 (a). b) Find the eigenvalues and eigenvectors of A. Diagonalize A. (c) Find a…

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Q: Find the dimension of the eigenspace corresponding to the eigenvalue i = -5. -5 0-5 0 -5

A: Answer - Given matrix             A = -5100-5000-5 Find the dimension of the eigenspace…

Q: Let A = PDP-1, where P is orthogonal and D is diagonal, and let a be an eigenvalue of A of…

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Q: If AB = BA, prove that A and B have a common eigenvector.

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Q: Is d=2 eigen value 3. an of 3.

A: Given matrix is,