Pertanyaan

Diketahui matriks A= ( 2 0 − 4 1 ) dan B= ( 1 3 3 − 8 ) . Invers dari matriks A= B adalah ...

Diketahui matriks A= $(20 - 41)$ dan B= $(13 3 - 8)$ . Invers dari matriks A= B adalah ...

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Pembahasan

$J i k a space C equals open parentheses table row cell a space space space b end cell row cell c space space space d end cell end table close parentheses comma space m a k a C to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar C close vertical bar end fraction A d j left parenthesis C right parenthesis A d j left parenthesis C right parenthesis equals open parentheses table row cell d space space space minus b end cell row cell negative c space space space a end cell end table close parentheses open vertical bar C close vertical bar equals d e t left parenthesis C right parenthesis equals a d minus b c M a k a colon C equals A plus B C equals open parentheses table row cell 2 space space space 0 end cell row cell negative 4 space space space space 1 end cell end table close parentheses plus open parentheses table row cell 1 space space space 3 end cell row cell 3 space space space minus 8 end cell end table close parentheses equals open parentheses table row cell 3 space space space 3 end cell row cell negative 1 space space space minus 7 end cell end table close parentheses open vertical bar C close vertical bar equals space d e t left parenthesis C right parenthesis equals space a d minus b c equals left parenthesis 3. left parenthesis negative 7 right parenthesis right parenthesis space minus space left parenthesis 3. left parenthesis negative 1 right parenthesis right parenthesis equals negative 21 minus left parenthesis negative 31 right parenthesis S e h i n g g a colon C to the power of negative 1 end exponent equals negative 1 over 18 open parentheses table row cell negative 7 space space space minus 3 end cell row cell 1 space space space space 3 end cell end table close parentheses equals negative 1 over 18 open parentheses table row cell negative 7 space space minus 3 end cell row cell 1 space space space space 3 end cell end table close parentheses$