(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...

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(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:0x—y+z—w=1x+y—z—w=1x—y—z—l—wzl (b) For two square matrices M, N of the same size, we define[M, N] = MN — NM. 0 1 00 1 0LL, 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