Part 3 Vector Calculus Answers and Explaination

QUESTION 19 Derivative of a vector with respect to a vector Choose one . 4 points W1 Calculate , if w = W2 where W1 +y + Z W2 = x + y + 2z and u = y Z O 0 0 0 0 O S 1 O\fQUESTION 21 Derivative of a scalar function with respect to a vector (Jacobian) Choose one . 4 points If sa =x2 + y' + (z - 1)2 where x = y then Z calculate O = [21 2y 2(z - 1)] [21 2y 2z] O 2y 2z\fQUESTION 23 Derivative of a scalar function with respect to a vector (Jacobian) Choose one . 4 points If g(x) - x2 + 2xy + 2 ac where x = y , then Z calculate Ox O = [2 + 2y 21 2z] O ag [2x + 2y 2y 2z] 21 + 2y 2y 2z\fQUESTION 25 Quadric form Choose one . 4 points Express the quadric form f(x, y) = 3x2 + 2xy + 6y in matrix form , fa) = x Ax where where * = y Z and calculate of ( ) = Ox O f(2) - 27 Am - of = [6 + 4y 4x + 12y] O of (2 8 ) O of = [6z + 2y 2x + 12y]