4. (25 pts) Let Q(x) = 2x +60 12-623. [ - ] (a) Compute the value of Q(x) for x = (b) Write Q(x) as x"Ax (c) Find the ei

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4 25 Pts Let Q X 2x 60 12 623 A Compute The Value Of Q X For X B Write Q X As X Ax C Find The Ei 1 (21.95 KiB) Viewed 18 times

4. (25 pts) Let Q(x) = 2x +60 12-623. [ - ] (a) Compute the value of Q(x) for x = (b) Write Q(x) as x"Ax (c) Find the eigenvalues of A. (d) Orthogonally diagonalize matrix A by finding an orthogonal matrix P and a diagonal matrix D such that A = PDP-1 (e) Make a change of variable that transforms Q(x) into a quadratic form with no cross- product term. (1) Determine whether Q(x) is positive definite, negative definite, or indefinite. State your reason