Question: For the matrix Find the eigenvalues ofA. Find the eigenvectors associated with each eigenvalue of A. If A is diagonalizable find the matrix P, such

For the matrix Find the eigenvalues ofA. Find the eigenvectors associated with each eigenvalue of A. If A is diagonalizable find the matrix P, such that P'lAP is a diagonal matrix. lfA is not diagonalizable, briefly explain why. If A is diagonalizable, find the diagonal matrix that would result from P'lAP. 1 2 1 Is the matrix A = 0 1 4 diagonalizable? Explain your answer. 0 0 2 Suppose that A = [g 12] is used to generate an inner product on R2, such that (11,1?) = Aii -A13. Use the given inner product to evaluate the following. a. Rewrite (17.13) as Matrix Multiplication. b. Ifi'I = L21] and 13 = [41], find the following: I. (1113) II. ll'll "I. Find the angle between the two vectors. IV. Verify the Cauchy Schwarz inequality for the two vectors V. Verify the Triangle inequality for the vectors

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