2. 3. Compute the values of the parameters for which the following quadratic form is positive definite: f(x, x2, x3) = x + x + 5x + 2x1x2 2x1x3 + 4x2x3. Compute the Hessian matrix of the function f(x) = (a x)(bx), where x, a, b E R" and both a and bare different from zero. Compute the rank of the matrix, assuming that a, b are linearly independent. Prove that if S is square n x n real matrix, which is symmetric and positive definite, then S is also positive definite and -S-Vf(x) is a descent direction at for any smooth function f : R" R.