Q1.

Let x = . Compute x Ax for the following matrices: LX2 a A = 2 1 1 4. 1 -3 b ) A = L-3 2Examine whether the following quadratic forms are positive definite, negative definite, or indefinite: (a) 6.x3+ 25x3 + 9x3 -60x2x3 + 40x1x3 - 6*1X2 b) 9x2 + 9x3 + 10x2x3 + 6x1X2Use theorem 11. 12 to show that the function f ( x , , x 2 ) = 4 34 defined on IR is quasiconcave 4 + + Theorem 11.12 Suppose that f is a function defined on R" and that f has continuous first- and second-order partial derivatives. Let H represent the bordered Hessian of f. (i) If [ H 2| > 0, [H 3) 0 (n even), 0, 0