Tentukan invers matriks berikut. a. (2 -1 1 5) b. (1/2 -1/3

a. [[5/11, 1/11], [-1/11, 2/11]], b. [[2/3, 2/3], [-2, 1]]

Pembahasan

Untuk mencari invers matriks ordo 2x2, kita gunakan rumus:
Jika matriks A = [[a, b], [c, d]], maka inversnya, A⁻¹ = (1 / det(A)) * [[d, -b], [-c, a]], di mana det(A) = ad - bc.

a. Matriks (2 -1 1 5)
Kita anggap matriks A = [[2, -1], [1, 5]].
Determinan (det(A)) = (2 * 5) - (-1 * 1) = 10 - (-1) = 10 + 1 = 11.
Invers matriks A adalah A⁻¹ = (1/11) * [[5, 1], [-1, 2]] = [[5/11, 1/11], [-1/11, 2/11]].

b. Matriks (1/2 -1/3 1 1/3)
Kita anggap matriks B = [[1/2, -1/3], [1, 1/3]].
Determinan (det(B)) = (1/2 * 1/3) - (-1/3 * 1) = 1/6 - (-1/3) = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.
Invers matriks B adalah B⁻¹ = (1 / (1/2)) * [[1/3, 1/3], [-1, 1/2]] = 2 * [[1/3, 1/3], [-1, 1/2]] = [[2/3, 2/3], [-2, 1]].

Jawaban:
a. [[5/11, 1/11], [-1/11, 2/11]]
b. [[2/3, 2/3], [-2, 1]]