Determinan Matriks 2 x 2, dan Perkaliannya

A. CARA MENGHITUNG

Misalkan A = abcd, sebuah matriks 2 x 2

Maka determinan A = ad – bc, atau hasil kali elemen diagonal I (miring ke kiri), dikurangi hasil kali diagonal II (miring ke kanan)

Contoh : A =  matriks-1234, maka det A = 1.4 – 2.3 = -2

PERKALIAN DETERMINAN 2 MATRIKS 2X2, APAKAH SAMA DENGAN DETERMINAN PERKALIAN 2 MATRIKS 2X2 Tersebut?

Mari kita lihat pembahasan berikut.

Misal kan matriks A =  abcdB = abcd

Determinan matriks A = (ad – bc), sedangkan determinan matriks B = (eh – fg)

Maka det A . det B = (ad – bc).(eh-fg) = adeh – bceh – adfg + bcfg

Sedangkan matriks A.B = abcd  x abcdabcddengan determinan (ae+bg)(cf+dh)-(af+bh)(ce+dg) = (acef + bcgf + adeh + bdgh) – (acef + bceh + adfg + bdgh) = bcgf – bceh – adfg + adeh = det A . det B

Maka, TERBUKTI, untuk setiap A dan B matriks berordo 2 x 2, det (A.B) = det A . det B.

2 thoughts on “Determinan Matriks 2 x 2, dan Perkaliannya

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