Diketahui vektor a = [a1 a2], b = [b1 b2] dan c = [2 5]. Jika a + b = c dan 4a - b = c, maka (a1-b1)/(a2-b2) = ... A. 4/5 B. 3/5 C. 2/5 D. 1/5 E. 6/5

Jawabannya adalah C. 2/5 Konsep A = [a b] , B =[c, d] A+B = [a+c b+d] kA = (ka kb) Jika A=B maka a=c, b=d a+b = c [a1 a2] + [b1 b2] = [2 5] [a1+b1 a2+b2] = [2 5] a1+b1 = 2....pers(1) a2+b2 = 5....pers(2) 4a - b = c 4[a1 a2] - [b1 b2] = [2 5] [4a1 4a2] - [b1 b2] = [2 5] [4a1-b1 4a2-b2] =[2 5] 4a1-b1 = 2...pers(3) 4a2-b2 = 5...pers(4) Eliminasi pers (1) dan pers(3) a1 + b1 = 2 4a1- b1 =2 _________+ 5a1 = 4 a1 = 4/5 a1+b1 = 2 4/5 + b1 = 2 b1 = 2- (4/5) b1 = 10/5 - (4/5) b1 = 6/5 Eliminasi pers(2) dan pers(4) a2+b2 = 5 4a2-b2 = 5 _________+ 5a2 = 10 a2 = 2 a2 + b2 = 5 2 + b2 = 5 b2 = 3 (a1-b1)/(a2-b2) =(4/5 - 6/5) / (2-3) =(-2/5) / (-1) = 2/5 Oleh karena itu jawaban yang benar adalah C. 2/5