Tentukan x,y dan z. [(x+y −3x−2z)(−3 2x+y)]−[(3x+4y y+z)(2 −x−y)]=[(−1 4)(−5 4)]

Jawaban yang benar adalah {(x, y, z) | (2, -1, 1)}. Sifat : Jika matriks A = [(a b) (c d)] dan matriks B = [(k l) (m n)], maka : A - B = [(a-k b-l) (c-m d-n)] A =B dengan a = k, b = l, c = m, d = n [(x+y −3x−2z) (−3 2x+y)] - [(3x+4y y+z) (2 −x−y)] = [(−1 4) (−5 4)] [(x+y-(3x+4y) -3x-2z-(y+z)) (-3-2 2x+y-(-x-y))] = [(-1 4) (-5 4)] [(x+y-3x-4y -3x-2z-y-z) (-3-2 2x+y+x+y)] = [(-1 4) (-5 4)] [(-2x -3y -3x-y-3z) (-5 3x+2y))] = [(-1 4) (-5 4)] • -2x - 3y = -1 ---> 2x + 3y = 1...(1) • -3x - y - 3z = 4 ... (2) • 3x + 2y = 4 ... (3) Eliminasi persamaan (1) dan (3) : 2x + 3y = 1 [dikali 3] 6x + 9y = 3 3x + 2y = 4 [dikali 2] 6x + 4y = 8 ———————————------------- - 5y = -5 y = -1 Substitusi nilai y ke persamaan (1) : 2x + 3y = 1 2x + 3(-1) = 1 2x - 3 = 1 2x = 4 x = 2 Substitusi nilai x dan y ke persamaan (2) : 3x - y - 3z = 4 3(2) - (-1) - 3z = 4 6 + 1 - 3z = 4 7 - 3z = 4 3 = 3z 1 = z Jadi, nilai x, y, dan z yang memenuhi adalah {(x, y, z) | (2, -1, 1)}.