Diketahui matriks A=(1 2 3 4) dan B=(1 y x 3). Jika

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Pembahasan

Diketahui matriks A = (1 2 3 4) dan B = (1 y x 3). Perkalian matriks AB adalah:
AB = [[(1*1) + (2*x)], [(1*y) + (2*3)]]
     [[(3*1) + (4*x)], [(3*y) + (4*3)]]
AB = [[1+2x, y+6]
     [3+4x, 3y+12]]

Determinan dari matriks AB adalah:
det(AB) = (1+2x)(3y+12) - (y+6)(3+4x)

Diketahui determinan AB = 10.
Maka, (1+2x)(3y+12) - (y+6)(3+4x) = 10
(3y + 12 + 6xy + 24x) - (3y + 4xy + 18 + 24x) = 10
3y + 12 + 6xy + 24x - 3y - 4xy - 18 - 24x = 10
(6xy - 4xy) + (24x - 24x) + (3y - 3y) + (12 - 18) = 10
2xy - 6 = 10
2xy = 10 + 6
2xy = 16
xy = 16 / 2
xy = 8