Problem 8. In each part, you are given a matrix A and its eigenvalues. Find a...

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Problem 8. In each part, you are given a matrix A and its eigenvalues. Find a basis for each of the eigenspaces of A and determine if A is If so, find a diagonal matrix D and an invertible matrix P so diagonalizable. that P-1AP = D. A. The matrix is A B. The matrix is and the eigenvalues are -1 and 2. 11 -3 -3 9 -1-3 27 -9 -7 A = -4 -1 4 -6-2 7 -6-16 and the eigenvalues are -1 and 2. Instructions: Use a calculator the find RREFs and to do matrix algebra. Otherwise, do the work by hand. (You can't use the eigenvalue and eigenvector functions on the calculator, which only give approximate answers in any case.) Problem 8. In each part, you are given a matrix A and its eigenvalues. Find a basis for each of the eigenspaces of A and determine if A is If so, find a diagonal matrix D and an invertible matrix P so diagonalizable. that P-1AP = D. A. The matrix is A B. The matrix is and the eigenvalues are -1 and 2. 11 -3 -3 9 -1-3 27 -9 -7 A = -4 -1 4 -6-2 7 -6-16 and the eigenvalues are -1 and 2. Instructions: Use a calculator the find RREFs and to do matrix algebra. Otherwise, do the work by hand. (You can't use the eigenvalue and eigenvector functions on the calculator, which only give approximate answers in any case.)

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