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For Problem 1 - 2 , 1 ) check if the given matrix is diagonalisable , and if so , 2 ) find out P and D satisfying A _ PDP - 1 Problem 1 . A = |1 1 1 I O Problem 2. A = 1 3 I 2 O Problem 3. Let A = 3 4 A. Observe that if AU = 10, then A3V = AZ . AU = AZ. ( 10 ) = 1A. (`AU ) = 12 AU = 135. Use Problem 2 and above observation ( but 5 instead of 3 ) to compute* Eigenvalues of A' and their corresponding eigenvectors .* B. Use your computation A _ PDP - 1 for P and D from Problem 2. Observe that A3 = ( PDP - 1 )3 = PD 3P- 1. Compute AS ( The same method as observation but 5 instead of 3 ) . C . Check that Eigenvalues and Eigenvectors you found in Problem 3 . A agree with the definition of Eigenvalues and Eigenvectors . That is , if He is an eigenvalue of A' and w is an eigenvector of A' corre - sponding to Me , then check A'W - NW.\f