19. (a) Suppose that A is an arbitrary square matrix. Show that x Ax > 0 for all x # 0 if and only if the symmetric matrix B = {(A + A¹) is positive definite. (Hint: Use the fact that (b) Show that if A x• Ax = A¹x.x = x• A¹x for all x.) 3 - (²4). = then x Ax> 0 for all x ‡ 0 in R².

Let A be a matrix and mathbfb be a matrix and a vector defined by 1 2 1 -1 1 b = 1 1 3 Compute x* that minimizes ||Ax - b|.