Nilai a, b, c, dan d jika (5 4 4 1)(a b c d)=(1 0 0 1)

a = -1/11, b = 4/11, c = 4/11, d = -5/11

Pembahasan

Kita memiliki persamaan matriks:
[5 4]
[4 1] * [a b]
      [c d] = [1 0]
                                         [0 1]

Kita dapat mengalikan kedua matriks di sisi kiri:
[5a + 4c   5b + 4d]
[4a + c    4b + d] = [1 0]
                                                 [0 1]

Dari kesamaan matriks tersebut, kita dapat membentuk sistem persamaan linear:
1) 5a + 4c = 1
2) 4a + c = 0  => c = -4a
3) 5b + 4d = 0
4) 4b + d = 1  => d = 1 - 4b

Substitusikan c = -4a ke persamaan (1):
5a + 4(-4a) = 1
5a - 16a = 1
-11a = 1
a = -1/11

Maka, c = -4a = -4(-1/11) = 4/11

Substitusikan d = 1 - 4b ke persamaan (3):
5b + 4(1 - 4b) = 0
5b + 4 - 16b = 0
-11b + 4 = 0
-11b = -4
b = 4/11

Maka, d = 1 - 4b = 1 - 4(4/11) = 1 - 16/11 = (11 - 16)/11 = -5/11

Jadi, nilai a = -1/11, b = 4/11, c = 4/11, dan d = -5/11.