Tentukan invers matriks-matriks berikut! a. A=(5 7 -3 -10)

Invers A = [[10/29, 7/29], [-3/29, -5/29]], Invers B = [[-5/4, 1], [-9/4, 2]]

Pembahasan

Untuk menentukan invers matriks ordo 2x2, misalnya matriks K = [[a, b], [c, d]], rumusnya adalah K⁻¹ = (1 / (ad - bc)) * [[d, -b], [-c, a]].

a. Matriks A = [[5, 7], [-3, -10]]
Determinan A (ad - bc) = (5)(-10) - (7)(-3) = -50 - (-21) = -50 + 21 = -29.
Invers A (A⁻¹) = (1 / -29) * [[-10, -7], [3, 5]] = [[-10/-29, -7/-29], [3/-29, 5/-29]] = [[10/29, 7/29], [-3/29, -5/29]].

b. Matriks B = [[-8, 4], [-9, 5]]
Determinan B (ad - bc) = (-8)(5) - (4)(-9) = -40 - (-36) = -40 + 36 = -4.
Invers B (B⁻¹) = (1 / -4) * [[5, -4], [9, -8]] = [[5/-4, -4/-4], [9/-4, -8/-4]] = [[-5/4, 1], [-9/4, 2]].