Application 8. Determine the intersection, if any, of each of the following sets of planes. In each case, give a geometrical interpretation of the system of equations and the solution. Also state whether the system has no solutions, a unique solution, or an infinite number of solutions. a. x + 2y + z = 12 2x - y + z = 5 3x + y - 2z = 1 d. -2x+4y+6z=-2 4x-8y-12z = 4 x-2y-3z=1 x-3y-2z=9 b. x y + 2z = 4 e. 2x-2y+4z=7 3x-3y+ 6z = 11 x + y + 2z = 2 x-y-2z = 5 C. x+y-z=5 2x + 2y - 4z = 6 x+y-2z = 3 f. x+3y+5z = 10 2x+6y+10z = 18 x + 3y+5z = 9 3.x + 3y+ 6z = 5 g. h. x+y+2z = 6 i. 2x + y + z = 0 x+11y+5z = -5 x-y-4z=-2 3x+5y+12z = 27 x-2y-3z = 0 3x + 2y + 4z = 0 2x + 8y + 3z = 4