(1) Let 'P be the plane given by 233 + y + 22 = 5. Let 73' 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'. (b) Show that the Cartesian equations for 'P and 'P' form an inconsistent system. (0) Let R be the point (2, 17 2). Calculate the distance from R to 'P'. (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 xyzlwzl (b) For two square matrices M, N of the same size, we dene [M, N] = MN NM. 0 1 00 1 0 LL, Gig/41 015mm, _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+ 6X + fY, [H,Y] = gH+hX+iY. Let