Pertanyaan

Diketahui matriks A = ( − 1 1 1 − 1 0 1 ) dan matriks B = ⎝ ⎛ 2 1 1 1 − 1 1 ⎠ ⎞ . Jika matriks C=AB, invers matriks C adalah C − 1 =.....

Diketahui matriks $A = (- 1 1 1 - 1 01)$ dan matriks $B = ⎝ ⎛ 211 1 - 1 1 ⎠ ⎞$ . Jika matriks C=AB, invers matriks C adalah $C^{- 1}$ =.....

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Pembahasan

$C equals A B C equals open parentheses table row cell negative 1 end cell 1 0 row 1 cell negative 1 end cell 1 end table close parentheses open parentheses table row 2 1 row 1 cell negative 1 end cell row 1 1 end table close parentheses C equals open parentheses table row cell negative 2 plus 1 plus 0 end cell cell negative 1 minus 1 plus 0 end cell row cell 2 minus 1 plus 1 end cell cell 1 plus 1 plus 1 end cell end table close parentheses C equals open parentheses table row cell negative 1 end cell cell negative 2 end cell row 2 3 end table close parentheses I n g a t space k e m b a l i space c a r a space i n v e r s space m a t r i k s space colon M equals open parentheses table row a b row c d end table close parentheses rightwards arrow M to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses M a k a space i n v e r s space d a r i space m a t r i k s space C space d i a t a s space a d a l a h C to the power of negative 1 end exponent equals fraction numerator 1 over denominator open parentheses negative 1 close parentheses open parentheses 3 close parentheses minus left parenthesis 2 right parenthesis left parenthesis negative 2 right parenthesis end fraction open parentheses table row 3 2 row cell negative 2 end cell cell negative 1 end cell end table close parentheses C to the power of negative 1 end exponent equals open parentheses table row 3 2 row cell negative 2 end cell cell negative 1 end cell end table close parentheses$