MATH 2153 Lecture 31: M2153 30 Divergence and Curl

A = (3 6 2 -1 -1 1 2 2 2 11 0 0 2 -3 4 1 2 0 5 7). Determine the subspace the following vectors belong to: v_1 = (0 0 0 0), v_2 = (0 0 0 0 0), v_3 = (2 3 -3 6), v_4 = (-1 2 -5 -2 1), v_5 = (0 4 -4 -4) and v_6 = (0 0 2 2 14).

The stationary points of the function f(x, y) = xy2 + x2 + 2y2 - 8 are: (0, 0), (-2, -2), (2, -2) (0, 0), (2, 2), (-2, 2) (0, 0), (-2, 2), (-2, -2) (0, -4), (-2, -2), (-2, 2) none of the above

Let W(s, t) = F(u(s, t), v(s, t)) where u(1, 0) = -2, us(1, 0) = -3, ut(1, 0) = -4 v(1, 0) = 2, vs(1, 0) = -2, vt(1, 0) = 0 Fu(-2, 2) = 5, Fv(-2, 2) = 2 Ws(1, 0) = Wt(1, 0) =