Question: 5. Given (2013, 1 Sem.) -1 2 0 A = 2 2 0 , x ERS and ||x|| = 1. 0 1. a. Decompose A

5. Given (2013, 1" Sem.) -1 2 0 A = 2 2 0 , x ERS and ||x|| = 1. 0 1. a. Decompose A into A=QAQ where Q is an orthonormal matrix and A is a diagonal matrix containing the eigenvalues of A. Then, decide if A is positive definite, negative definite or indefinite. b. What are the maximum, minimum and minimum absolute value of x Ax? c. Find a vector x that gives the minimum absolute value of x Ax (the answer is not unique and any valid answer will do)

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