Diketahui matriks A = (1 -1 2 3), B = (-7 -3 11 14), X =(a

Nilai d adalah 4.

Pembahasan

Untuk menyelesaikan matriks AX = B, kita perlu mencari matriks X. Pertama, kita tentukan matriks A dan B:
A = [[1, -1],
     [2,  3]]
B = [[-7, -3],
     [11, 14]]
Karena AX = B, maka X = A⁻¹B. Untuk mencari invers matriks A (A⁻¹), kita gunakan rumus:
A⁻¹ = (1 / det(A)) * [[d, -b],
                     [-c, a]]

Dengan a=1, b=-1, c=2, d=3, maka:
det(A) = ad - bc = (1)(3) - (-1)(2) = 3 - (-2) = 3 + 2 = 5
A⁻¹ = (1/5) * [[3, 1],
              [-2, 1]]

Sekarang kita hitung X = A⁻¹B:
X = (1/5) * [[3, 1],
              [-2, 1]] * [[-7, -3],
                                    [11, 14]]

X = (1/5) * [[(3*-7 + 1*11), (3*-3 + 1*14)],
              [(-2*-7 + 1*11), (-2*-3 + 1*14)]]

X = (1/5) * [[(-21 + 11), (-9 + 14)],
              [(14 + 11), (6 + 14)]]

X = (1/5) * [[-10, 5],
              [25, 20]]

X = [[-10/5, 5/5],
     [25/5, 20/5]]

X = [[-2, 1],
     [5, 4]]

Jadi, matriks X = [[a, b],
                  [c, d]] = [[-2, 1],
                                          [5, 4]].
Nilai d pada matriks X adalah 4.