Question: 3. Consider the matrix A = 2 12 2 . It is given that the eigenvalues of A are -1 and 5. (a) (5 pts)

3. Consider the matrix A = 2 12 2 . It is given that the eigenvalues of A are -1 and 5. (a) (5 pts) Find a basis for the eigenspace corresponding to each eigenvalue of A. (b) (10 pts) Orthogonally diagonalize A. That is, find an orthogonal matrix P and a diagonal matrix D such that A = PDP-1. (c) (5pts) What is the canonical form (that is, the form with no cross-product term) of q(x) = x' Ax? Is q(x) positive indefinite, negative indefinite, or indefinite

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