Diketahui matriks A=(4 3 2 2) dan B=(-2 -3 3 5). Jika

C^-1 = [-26 -21] [ 16 13 ]

Pembahasan

Untuk menyelesaikan soal ini, kita perlu mencari invers dari matriks C, di mana C = A^-1 B. Langkah-langkahnya adalah sebagai berikut:

1. Cari invers dari matriks A (A^-1).
   Matriks A = [4  3]
               [2  2]
   Determinan A = (4 * 2) - (3 * 2) = 8 - 6 = 2
   A^-1 = 1/det(A) * [ d -b]
                      [-c  a]
   A^-1 = 1/2 * [ 2 -3]
                 [-2  4]
   A^-1 = [ 1 -3/2]
          [-1  2]

2. Hitung matriks C = A^-1 B.
   C = [ 1 -3/2] * [-2 -3]
       [-1  2]    [ 3  5]
   C = [ (1*-2 + -3/2*3)  (1*-3 + -3/2*5) ]
       [ (-1*-2 + 2*3)   (-1*-3 + 2*5)  ]
   C = [ (-2 - 9/2)  (-3 - 15/2) ]
       [ (2 + 6)     (3 + 10)   ]
   C = [ (-4/2 - 9/2)  (-6/2 - 15/2) ]
       [ 8           13           ]
   C = [ -13/2 -21/2 ]
       [ 8    13     ]

3. Cari invers dari matriks C (C^-1).
   Determinan C = (-13/2 * 13) - (-21/2 * 8)
   Determinan C = -169/2 - (-168/2)
   Determinan C = -169/2 + 168/2
   Determinan C = -1/2

   C^-1 = 1/det(C) * [ d -b]
                      [-c  a]
   C^-1 = 1/(-1/2) * [ 13  21/2 ]
                     [ -8  -13/2 ]
   C^-1 = -2 * [ 13  21/2 ]
             [ -8  -13/2 ]
   C^-1 = [ -26 -21 ]
          [ 16  13  ]

Jadi, matriks C^-1 adalah [-26 -21]
                            [ 16  13 ].