Page 3 of 5 2 2 (20pts) 3. Consider the matrix A = 2 2 . It is given that the eigenvalues of A are -1 and 5. 2 (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