Tentukan invers matriks berikut. a. (-16 19 5 -6) b. (3 -2

a. [[-6, -19], [-5, -16]], b. [[-5, 2], [-8, 3]]

Pembahasan

Untuk mencari invers matriks ordo 2x2, misalnya matriks M = [[a, b], [c, d]], rumusnya adalah M⁻¹ = (1/det(M)) * [[d, -b], [-c, a]], di mana det(M) = ad - bc.

a. Matriks = [[-16, 19], [5, -6]]
Determinan (det) = (-16)(-6) - (19)(5)
Det = 96 - 95
Det = 1

Invers matriks = (1/1) * [[-6, -19], [-5, -16]]
Invers matriks = [[-6, -19], [-5, -16]]

b. Matriks = [[3, -2], [8, -5]]
Determinan (det) = (3)(-5) - (-2)(8)
Det = -15 - (-16)
Det = -15 + 16
Det = 1

Invers matriks = (1/1) * [[-5, 2], [-8, 3]]
Invers matriks = [[-5, 2], [-8, 3]]