Diketahui persamaan matriks 3[(4 1)(6 b)]+[(3a 5)(1 4)]=[(2 1)(5 4)][(3 2)(1 4)] Nilai dari 3a+3b adalah ...

Jawabannya adalah 17 Konsep A =[(a b) (c d)], B =[(e f) (g h)] AB= [(ae+bg af+bh) (ce+dg cf+dh)] kA =[(ka kb) (kc kd)] A+B =[(a+e b+f) (c+g d+h)] Jika A=B, maka a=e, b=f, c=g, d=h 3[(4 1)(6 b)]+[(3a 5)(1 4)]=[(2 1)(5 4)][(3 2)(1 4)] [(12 3)(18 3b)]+[(3a 5)(1 4)]=[(2.3+1.1 2.2+1.4)(5.3+4.1 5.2+4.4)] [(12 3)(18 3b)]+[(3a 5)(1 4)]=[(7 8)(19 26)] [(12+3a 8)(19 3b+4)]=[(7 8)(19 26)] 12+3a =7 3a = 7-12 3a = - 5 a = - 5/3 3b+4 = 26 3b = 26-4 3b = 22 b = 22/3 3a + 3b = 3(-5/3) +3(22/3) = - 5+ 22 = 17 Jadi jawabnya 3a +3b = 17