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Pergunakan prinsip kofaktor-minor untuk menentukan invers matriks berikut. ⎝ ⎛ ​ 1 2 3 ​ − 2 − 1 − 3 ​ − 3 − 4 − 5 ​ ⎠ ⎞ ​

Pergunakan prinsip kofaktor-minor untuk menentukan invers matriks berikut.

 

 

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A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Pembahasan

Menentukan determinan Menentukan kofaktor Menentukan adjoin Menentukan invers matriks Kesimpulan

Menentukan determinan

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell determinan space colon end cell row blank blank cell open vertical bar table row 1 cell negative 2 end cell cell negative 3 end cell row 2 cell negative 1 end cell cell negative 4 end cell row 3 cell negative 3 end cell cell negative 5 end cell end table close vertical bar table row 1 cell negative 2 end cell row 2 cell negative 1 end cell row 3 cell negative 3 end cell end table end cell row blank equals cell open square brackets open parentheses 1. negative 1. negative 5 close parentheses plus open parentheses negative 2. negative 4.3 close parentheses plus open parentheses negative 3.2. negative 3 close parentheses close square brackets minus open square brackets open parentheses 3. negative 1. negative 3 close parentheses plus open parentheses negative 3. negative 4.1 close parentheses plus open parentheses negative 5.2. negative 2 close parentheses close square brackets end cell row blank equals cell open square brackets 5 plus open parentheses 24 close parentheses plus 18 close square brackets minus open square brackets 9 plus open parentheses 12 close parentheses plus 20 close square brackets end cell row blank equals cell 47 minus 41 end cell row blank equals 6 row blank blank blank end table    

Menentukan kofaktor

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell Kofaktor space colon end cell row cell open vertical bar table row cell plus open vertical bar table row cell negative 1 end cell cell negative 4 end cell row cell negative 3 end cell cell negative 5 end cell end table close vertical bar end cell cell negative open vertical bar table row 2 cell negative 4 end cell row 3 cell negative 5 end cell end table close vertical bar end cell cell plus open vertical bar table row 2 cell negative 1 end cell row 3 cell negative 3 end cell end table close vertical bar end cell row cell negative open vertical bar table row cell negative 2 end cell cell negative 3 end cell row cell negative 3 end cell cell negative 5 end cell end table close vertical bar end cell cell plus open vertical bar table row cell negative 1 end cell cell negative 3 end cell row 3 cell negative 5 end cell end table close vertical bar end cell cell negative open vertical bar table row 1 cell negative 2 end cell row 3 cell negative 3 end cell end table close vertical bar end cell row cell plus open vertical bar table row cell negative 2 end cell cell negative 3 end cell row cell negative 1 end cell cell negative 4 end cell end table close vertical bar end cell cell negative open vertical bar table row 1 cell negative 3 end cell row 2 cell negative 4 end cell end table close vertical bar end cell cell plus open vertical bar table row 1 cell negative 2 end cell row 2 cell negative 1 end cell end table close vertical bar end cell end table close vertical bar end cell equals cell open vertical bar table row cell negative 7 end cell cell negative 2 end cell cell negative 3 end cell row cell negative 1 end cell 14 cell negative 3 end cell row 5 cell negative 2 end cell 3 end table close vertical bar end cell row blank blank blank row blank blank blank end table   

Menentukan adjoin

table attributes columnalign right center left columnspacing 0px end attributes row cell Adjoin space end cell equals cell transpose space dari space kofaktor end cell row blank equals cell open vertical bar table row cell negative 7 end cell cell negative 1 end cell 5 row cell negative 2 end cell 1 cell negative 2 end cell row cell negative 3 end cell cell negative 3 end cell 6 end table close vertical bar end cell end table 

  

Menentukan invers matriks

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell 1 over determinan cross times adjoin end cell row blank equals cell 1 over 6 open square brackets table row cell negative 7 end cell cell negative 1 end cell 5 row cell negative 2 end cell 1 cell negative 2 end cell row cell negative 3 end cell cell negative 3 end cell 6 end table close square brackets end cell row blank blank blank end table 

Kesimpulan 

Jadi space inversnya space adalah space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 6 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell negative 7 end cell cell negative 1 end cell 5 row cell negative 2 end cell 1 cell negative 2 end cell row cell negative 3 end cell cell negative 3 end cell 6 end table close square brackets end cell end table    

 

 

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