Linear Algebra Questions

2 5 0 4. Consider the matrix A = [4 3 0]. 0 0 1 a. Determine the eigenvalues of A. b. For each eigenvalue in a., determine a basis for the corresponding eigenspace. c. Is A diagonalizable? If so find an invertible matrix P and diagonal matrix D such that P'lAP = D. (You should not have to find P'1 to do thisl) 5 3 1 5. Consider the matrix A = [0 5 0]. 0 0 5 a. Determine the eigenvalues of A. b. For each eigenvalue in a., determine a basis for the corresponding eigenspace. c. Is A diagonalizable? If so find an invertible matrix P and diagonal matrix D such that P'lAP = D. (You should not have to find P'1 to do thisl) 000 200 044' 00-h 6. Consider the matrix A = 0 0 1 4- a. Determine the eigenvalues of A. b. For each eigenvalue in a., determine a basis for the corresponding eigenspace. c. Is A diagonalizable? If so find an invertible matrix P and diagonal matrix D Such that P'lAP = D. (You should not have to find P'1 to do thisl)