Question: -2 3 1. (5 points) Consider the matrix A = 0 4 3 Determine if A is diagonalizable. If A is 0 -2 diagonalizable, then

-2 3 1. (5 points) Consider the matrix A = 0 4 3 Determine if A is diagonalizable. If A is 0 -2 diagonalizable, then find a matrix P such that P-1AP is diagonal. If A is not diagonalizable, then briefly explain why. 0 2\\ 2. (5 points) Consider the matrix A = 1 0 Determine if A is diagonalizable. If A is 2 0 1 diagonalizable, then find a matrix P such that P-1AP is diagonal. If A is not diagonalizable, then briefly explain why. (5 points) 3. (10 points) Consider the vector space M2x2. a. Show that (A, B) = 2011b11 + a21b21 + @1212 + 2azzb22 defines and inner product on M2x2. b. Using the inner product defined above and the matrices A = B = (1 - 2) C = 60 1 ) find the following: ||All, d(A, B), and (B, C). (5 points each) c. What does (B, C) tell you about the relationship between the two matrices

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