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Invers dari matriks B = adalah…

Invers dari matriks B equals open square brackets table row 1 3 4 row 3 cell negative 1 end cell 6 row cell negative 1 end cell 5 6 end table close square brackets adalah…

  1. open square brackets table row cell 15 over 2 end cell cell negative 3 end cell cell negative 9 end cell row cell 3 over 2 end cell cell negative 1 half end cell cell negative 2 end cell row 1 5 1 end table close square brackets

  2. open square brackets table row cell 9 over 2 end cell cell negative 5 end cell cell negative 3 over 2 end cell row cell negative 1 end cell 7 cell 5 over 2 end cell row 3 11 4 end table close square brackets

  3. open square brackets table row cell 31 over 2 end cell cell negative 17 over 2 end cell cell negative 11 end cell row cell 9 over 2 end cell cell negative 5 over 2 end cell cell negative 3 end cell row cell negative 7 end cell 4 5 end table close square brackets

  4. open square brackets table row cell negative 5 end cell 4 cell 5 over 2 end cell row cell 9 over 2 end cell cell negative 11 end cell cell 2 over 3 end cell row 7 cell 1 third end cell cell negative 1 end cell end table close square brackets

  5. open square brackets table row cell 6 over 7 end cell cell negative 1 over 21 end cell cell negative 11 over 21 end cell row cell 25 over 42 end cell cell negative 5 over 21 end cell cell negative 1 over 7 end cell row cell negative 1 third end cell cell 4 over 21 end cell cell 5 over 21 end cell end table close square brackets

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Pembahasan

Determinan B Kofaktor B Adjoin B B invers

B equals open square brackets table row 1 3 4 row 3 cell negative 1 end cell 6 row cell negative 1 end cell 5 6 end table close square brackets B to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar B close vertical bar end fraction A d j space B

  • Determinan B

open vertical bar B close vertical bar equals 1 open vertical bar table row cell negative 1 end cell 6 row 5 6 end table close vertical bar minus 3 open vertical bar table row 3 6 row cell negative 1 end cell 6 end table close vertical bar plus 4 open vertical bar table row 3 cell negative 1 end cell row cell negative 1 end cell 5 end table close vertical bar space space space space space space space equals open parentheses negative 6 minus 30 close parentheses minus 3 open parentheses 18 plus 6 close parentheses plus 4 open parentheses 15 minus 1 close parentheses space space space space space space space equals negative 36 minus 3 open parentheses 24 close parentheses plus 4 open parentheses 14 close parentheses space space space space space space space equals negative 36 minus 72 plus 56 equals negative 42

  • Kofaktor B

K o f space B equals open square brackets table row cell plus open vertical bar table row cell negative 1 end cell 6 row 5 6 end table close vertical bar end cell cell negative open vertical bar table row 3 6 row cell negative 1 end cell 6 end table close vertical bar end cell cell plus open vertical bar table row 3 cell negative 1 end cell row cell negative 1 end cell 5 end table close vertical bar end cell row cell negative open vertical bar table row 3 4 row 5 6 end table close vertical bar end cell cell plus open vertical bar table row 1 4 row cell negative 1 end cell 6 end table close vertical bar end cell cell negative open vertical bar table row 1 3 row cell negative 1 end cell 5 end table close vertical bar end cell row cell plus open vertical bar table row 3 4 row cell negative 1 end cell 6 end table close vertical bar end cell cell negative open vertical bar table row 1 4 row 3 6 end table close vertical bar end cell cell plus open vertical bar table row 1 3 row 3 cell negative 1 end cell end table close vertical bar end cell end table close square brackets space space space space space space space space space space space space space equals open square brackets table row cell left parenthesis negative 6 minus 30 right parenthesis end cell cell negative left parenthesis 18 plus 6 right parenthesis end cell cell left parenthesis 15 minus 1 right parenthesis end cell row cell negative left parenthesis 18 minus 20 right parenthesis end cell cell left parenthesis 6 plus 4 right parenthesis end cell cell negative left parenthesis 5 plus 3 right parenthesis end cell row cell left parenthesis 18 plus 4 right parenthesis end cell cell negative left parenthesis 6 minus 12 right parenthesis end cell cell left parenthesis negative 1 minus 9 right parenthesis end cell end table close square brackets space space space space space space space space space space space space equals open square brackets table row cell negative 36 end cell cell negative 25 end cell 14 row 2 10 cell negative 8 end cell row 22 6 cell negative 10 end cell end table close square brackets

  • Adjoin B

A d j space B equals open parentheses K o f space B close parentheses to the power of T space space space space space space space space space space space space equals open square brackets table row cell negative 36 end cell 2 22 row cell negative 25 end cell 10 6 row 14 cell negative 8 end cell cell negative 10 end cell end table close square brackets

  • B invers

B to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar B close vertical bar end fraction A d j B space space space space space space space space equals fraction numerator 1 over denominator negative 42 end fraction open square brackets table row cell negative 36 end cell 2 22 row cell negative 25 end cell 10 6 row 14 cell negative 8 end cell cell negative 10 end cell end table close square brackets space space space space space space space space equals open square brackets table row cell 36 over 42 end cell cell negative 2 over 42 end cell cell negative 22 over 42 end cell row cell 25 over 42 end cell cell negative 10 over 42 end cell cell negative 6 over 42 end cell row cell negative 14 over 42 end cell cell 8 over 42 end cell cell 10 over 42 end cell end table close square brackets space space space space space space space equals open square brackets table row cell 6 over 7 end cell cell negative 1 over 21 end cell cell negative 11 over 21 end cell row cell 25 over 42 end cell cell negative 5 over 21 end cell cell negative 1 over 7 end cell row cell negative 1 third end cell cell 4 over 21 end cell cell 5 over 21 end cell end table close square brackets

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