Al. (a) Find the determinant of the matrix 1 2 1 1 2 2 1 0 A= 3 6 1 u 0 0 u v Sketch in a uv-plane the set of points for which A has no inverse. Hence, or otherwise, show that when v > > , A has an inverse for all values of u. (b) Consider the two quadratic forms r(X, X2 , X 3 ) = X, +xz + x3 - 2xX2. Determine directly from the definitions whether each quadratic form is (i) positive definite, (ii) positive semidefinite but not positive definite, (iii) neither of these