Find the real eigenvalues of the matrix [-11 -14 -10 1 -1 A 4 -1 6. 3 4 -1 4 The real eigenvalues are (Enter your answers as a comma separated list.)

For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) -1 0 0 2 15 501 P = A = ↓↑ Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 11 and -7 18 4 81 4 -5 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices) 4

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