Tentukan invers matriks-matriks berikut! g. L = ⎝ ⎛ ​ 8 2 0 ​ − 11 7 1 ​ 9 2 0 ​ ⎠ ⎞ ​

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Ingat kembali: A = ⎝ ⎛ ​ a d g ​ b e h ​ c f i ​ ⎠ ⎞ ​ → A − 1 = det ( A ) 1 ​ ( Adj ( A ) ) dimana: det ( A ) = ( a e i + b f g + c d h ) − ( ce g + a f h + b d i ) Diketahui matriks , maka: Menentukan Determinan Matriks det ( L ) ​ = = = = = ​ ( a e i + b f g + c d h ) − ( ce g + a f h + b d i ) ( 8 ⋅ 7 ⋅ 0 + − 11 ⋅ 2 ⋅ 0 + 9 ⋅ 2 ⋅ 1 ) − ( 9 ⋅ 7 ⋅ 0 + 8 ⋅ 2 ⋅ 1 + − 4 ⋅ 2 ⋅ 0 ) ( 0 − 0 + 18 ) − ( 0 + 16 − 0 ) 18 − 16 2 ​ Menentukan Kofaktor Matriks k of ( L ) ​ = = = ​ ⎝ ⎛ ​ + ∣ ∣ ​ 7 1 ​ 2 0 ​ ∣ ∣ ​ − ∣ ∣ ​ − 11 1 ​ 9 0 ​ ∣ ∣ ​ + ∣ ∣ ​ − 11 7 ​ 9 2 ​ ∣ ∣ ​ ​ − ∣ ∣ ​ 2 0 ​ 2 0 ​ ∣ ∣ ​ + ∣ ∣ ​ 8 0 ​ 9 0 ​ ∣ ∣ ​ − ∣ ∣ ​ 8 0 ​ 9 0 ​ ∣ ∣ ​ ​ + ∣ ∣ ​ 2 0 ​ 7 1 ​ ∣ ∣ ​ − ∣ ∣ ​ 8 0 ​ − 11 1 ​ ∣ ∣ ​ + ∣ ∣ ​ 8 2 ​ − 11 7 ​ ∣ ∣ ​ ​ ⎠ ⎞ ​ ⎝ ⎛ ​ + ( 0 − 2 ) − ( 0 − 9 ) + ( − 22 − 63 ) ​ − ( 0 − 0 ) + ( 0 − 0 ) − ( 0 − 0 ) ​ + ( 2 − 0 ) − ( 8 − 0 ) + ( 56 − ( − 22 ) ) ​ ⎠ ⎞ ​ ⎝ ⎛ ​ − 2 − 9 − 85 ​ 0 0 0 ​ 2 − 8 78 ​ ⎠ ⎞ ​ ​ Menentukan Adjoin Matriks Adj ( L ) ​ = = = ​ ( k of ( L ) ) T ⎝ ⎛ ​ − 2 − 9 − 85 ​ 0 0 0 ​ 2 − 8 78 ​ ⎠ ⎞ ​ T ⎝ ⎛ ​ − 2 0 2 ​ − 9 0 − 8 ​ − 85 0 78 ​ ⎠ ⎞ ​ ​ Sehingga: L − 1 ​ = = ​ d e t ( L ) 1 ​ ( Adj ( L ) ) 2 1 ​ ⎝ ⎛ ​ − 2 0 2 ​ − 9 0 − 8 ​ − 85 0 78 ​ ⎠ ⎞ ​ ​ Jadi, invers matriks adalah L − 1 ​ = ​ 2 1 ​ ⎝ ⎛ ​ − 2 0 2 ​ − 9 0 − 8 ​ − 85 0 78 ​ ⎠ ⎞ ​ ​ .