Question: (5) (8 marks) A symmetric matrix A has eigenvalues A1 = 3 and 12 = -1 and is a basis for E3 and E_1 has

(5) (8 marks) A symmetric matrix A has eigenvalues A1 = 3 and 12 = -1 and is a basis for E3 and E_1 has as a basis. (a) (4 marks) Find an orthogonal matrix Q and a diagonal matrix D such that AT AQ = D. (b) (4 marks) Use the previous part to find the matrix A as well as A-1. (To find A-] you are not allowed to use Gauss-Jordan Elimination rule)

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