(1) Let P be the plane given by 2x + y + 2z = 5. Let P 0 be the plane with the same normal vectors as P but through the point Q(2, 0, 4). (a) Find a Cartesian equation for P 0 . (b) Show that the Cartesian equations for P and P 0 form an inconsistent system. (c) Let R be the point (2, 1, 2). Calculate the distance from R to P 0 . (2) (a) Solve the following system of linear equations for x, y, z and w. x+y+z+w =0 xy+zw =1 x+yzw =1 x y z + w = 1 (b) For two square matrices M, N of the same size, we define [M, N ] = M N N M. Let \u0014 \u0015 \u0014 \u0015 \u0014 \u0015 0 1 0 0 1 0 X= ,Y = and H = . 0 0 1 0 0 1 Calculate constants a, b, c, d, e, f, g, h and i such that the following equations hold: [X, Y ] = aH + bX + cY, [H, X] = dH + eX + f Y, [H, Y ] = gH + hX + iY