Diketahui matriks P=[(3 7)(−2 1)] dan Q=[(2 −1)(3 1)]. Tentukan invers matriks (P+2Q)!

Halo Niko N :) Jawaban: [(3 -5)(-4 7)] Rumus untuk menentukan invers dari suatu matriks 2x2 adalah sebagai berikut: X = [(a b)(c d)] X⁻¹ = det X [(d -b)(-c a)] X⁻¹ = [(d(det X) -b(det X))(-c(det X) a(det X))] dimana det X = ad-bc perhatikan juga konsep penjumlahan matriks berikut: = [(a b)(c d)] + [(e f)(g h)] = [(a+e b+f)(c+g d+h)] Diketahui matriks P=[(3 7)(−2 1)] dan Q=[(2 −1)(3 1)]; maka nilai mariks P+2Q = [(3 7)(−2 1)] + (2)[(2 −1)(3 1)] = [(3 7)(−2 1)] + [(2(2) −1(2))(3(2) 1(2))] = [(3 7)(−2 1)] + [(4 −2)(6 2)] = [(3+4 7+(-2))(−2+6 1+2)] = [(7 5)(4 3)] maka invers dari matriks P+2Q adalah = (det P+2Q) [(3 -5)(-4 7)] = (7(3)-5(4)) [(3 -5)(-4 7)] = (21-20) [(3 -5)(-4 7)] = (1) [(3 -5)(-4 7)] = [(3(1) -5(1))(-4(1) 7(1))] = [(3 -5)(-4 7)] Jadi, nilai invers matriks (P+2Q) = [(3 -5)(-4 7)]