Let A = Find P1, the projection matrix on R(A). Find P2, the projection matrix on N(AT). Let x = [x1 X2 x3]T R3, find x1= projR(A)(x) and x2= projN(AT)(x). Verify that ATx2 = 0, where x2= projN(AT)(x). Verify that x = x1 + x2, where x1= projR(A)(x) and x2= projN(AT)(x). Determine, P1 and P2, the projection matrices on R(A) and N(AT) respectively, where A is an n times n nonsingular matrix.