Prove that x = (1, 0.5, -1) is optimal for the following optimization problem 1 2 where Hint: A0 A = are positive. min S.t. 13 12 xAx xAx + bx 1 i 1, i = 1,2,3, 12 -2 17 6 12 -2 6 and b = all its principle minors are nonnegative; A> 0 all its leading principle minors A principal submatrix of an n x n matrix is obtained by deleting of any k rows and corresponding k columns. -22 -14.5 13 The determinant of a principal submatrix is called the principal minor of A. The leading principal submatrix of order k of an n x n matrix is obtained by deleting the last n-k rows and column of the matrix.