Pertanyaan

Invers dari matriks A = ⎝ ⎛ 1 − 2 1 2 1 2 1 2 3 ⎠ ⎞ adalah...

Invers dari matriks $A = ⎝ ⎛ 1 - 2 1 212123 ⎠ ⎞$ adalah...

A. Acfreelance

Master Teacher

Jawaban terverifikasi

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Penyelesaian:

$open vertical bar A close vertical bar space equals space 3 space plus space 4 space minus space 4 space minus space 1 minus 4 minus left parenthesis negative space 12 right parenthesis space equals space 10 A d j space left parenthesis A right parenthesis equals space open parentheses table row cell open vertical bar table row 1 2 row 2 3 end table close vertical bar end cell cell negative open vertical bar table row 2 1 row 2 3 end table close vertical bar end cell cell open vertical bar table row 2 1 row 1 2 end table close vertical bar end cell row cell negative open vertical bar table row cell negative 2 end cell 2 row 1 3 end table close vertical bar end cell cell open vertical bar table row 1 1 row 1 3 end table close vertical bar end cell cell negative open vertical bar table row 1 1 row cell negative 2 end cell 2 end table close vertical bar end cell row cell open vertical bar table row cell negative 2 end cell 1 row 1 2 end table close vertical bar end cell cell negative open vertical bar table row 1 2 row 1 2 end table close vertical bar end cell cell open vertical bar table row 1 2 row cell negative 2 end cell 1 end table close vertical bar end cell end table close parentheses equals open parentheses table row cell 3 minus 4 end cell cell negative left parenthesis 6 minus 2 right parenthesis end cell cell 4 minus 1 end cell row cell negative left parenthesis negative 6 minus 2 right parenthesis end cell cell 3 minus 1 end cell cell negative left parenthesis 2 plus 2 right parenthesis end cell row cell negative 4 minus 1 end cell cell negative left parenthesis 2 minus 2 right parenthesis end cell cell 1 plus 4 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell cell negative 4 end cell 3 row 8 2 cell negative 4 end cell row cell negative 5 end cell 0 5 end table close parentheses A to the power of negative 1 end exponent equals fraction numerator 1 over denominator d e t left parenthesis A right parenthesis end fraction a d j left parenthesis A right parenthesis equals 1 over 10 open parentheses table row cell negative 1 end cell cell negative 4 end cell 3 row 8 2 cell negative 4 end cell row cell negative 5 end cell 0 5 end table close parentheses equals open parentheses table row cell negative 0 comma 1 end cell cell negative 0 comma 4 end cell cell 0 comma 3 end cell row cell 0 comma 8 end cell cell 0 comma 2 end cell cell negative 0 comma 4 end cell row cell negative 0 comma 5 end cell 0 cell 0 comma 5 end cell end table close parentheses$