1. Let A be an order 3 symmetric matrix. Suppose A has eigenvalues -1, 1 and...

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1. Let A be an order 3 symmetric matrix. Suppose A has eigenvalues -1, 1 and 2, with eigenvector (-) associated to 1. V_1=1 associated to -1 and v = 2 (a) (2 points) Write down the characteristic polynomial of A. (b) (5 points) Find an eigenvector associated to eigenvalue 2. Explain how you derive your answer. (c) (3 points) Hence, write A as PDPT for some orthogonal matrix P and diagonal matrix D. 1. Let A be an order 3 symmetric matrix. Suppose A has eigenvalues -1, 1 and 2, with eigenvector (-) associated to 1. V_1=1 associated to -1 and v = 2 (a) (2 points) Write down the characteristic polynomial of A. (b) (5 points) Find an eigenvector associated to eigenvalue 2. Explain how you derive your answer. (c) (3 points) Hence, write A as PDPT for some orthogonal matrix P and diagonal matrix D.