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Tentukan invers dari masing-masing matriks persegi berikut. ⎝ ⎛ ​ 1 − 3 2 ​ 0 − 1 1 ​ − 2 6 − 5 ​ ⎠ ⎞ ​

Tentukan invers dari masing-masing matriks persegi berikut.

 

 

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A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

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 0 cell negative 2 end cell row cell negative 3 end cell cell negative 1 end cell 6 row 2 1 cell negative 5 end cell end table close vertical bar table row 1 0 row cell negative 3 end cell cell negative 1 end cell row 2 1 end table end cell row blank equals cell open square brackets open parentheses 1. negative 1. negative 5 close parentheses plus open parentheses 0.6.2 close parentheses plus open parentheses negative 2. negative 3.1 close parentheses close square brackets minus open square brackets open parentheses 2. negative 1. negative 2 close parentheses plus open parentheses 1.6.1 close parentheses plus open parentheses negative 5. negative 3.0 close parentheses close square brackets end cell row blank equals cell open square brackets 5 plus 0 plus 6 close square brackets minus open square brackets 4 plus 6 plus 0 close square brackets end cell row blank equals cell 11 minus 10 end cell row blank equals 1 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 6 row 1 cell negative 5 end cell end table close vertical bar end cell cell negative open vertical bar table row cell negative 3 end cell 6 row 2 cell negative 5 end cell end table close vertical bar end cell cell plus open vertical bar table row cell negative 3 end cell cell negative 1 end cell row 2 1 end table close vertical bar end cell row cell negative open vertical bar table row 0 cell negative 2 end cell row 1 cell negative 5 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 5 end cell end table close vertical bar end cell cell negative open vertical bar table row 1 0 row 2 1 end table close vertical bar end cell row cell plus open vertical bar table row 0 cell negative 2 end cell row cell negative 1 end cell 6 end table close vertical bar end cell cell negative open vertical bar table row 1 cell negative 2 end cell row cell negative 3 end cell 6 end table close vertical bar end cell cell plus open vertical bar table row 1 0 row cell negative 3 end cell 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 1 cell negative 3 end cell 1 row cell negative 2 end cell 1 cell negative 1 end cell row 2 0 1 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 1 cell negative 2 end cell 2 row cell negative 3 end cell 1 0 row 1 cell negative 1 end cell 1 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 determinan open square brackets table row 1 cell negative 2 end cell 2 row cell negative 3 end cell 1 0 row 1 cell negative 1 end cell 1 end table close square brackets end cell row blank equals cell 1 over 1 open square brackets table row 1 cell negative 2 end cell 2 row cell negative 3 end cell 1 0 row 1 cell negative 1 end cell 1 end table close square brackets end cell row blank equals cell open square brackets table row 1 cell negative 2 end cell 2 row cell negative 3 end cell 1 0 row 1 cell negative 1 end cell 1 end table close square brackets end cell 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 open square brackets table row 1 cell negative 2 end cell 2 row cell negative 3 end cell 1 0 row 1 cell negative 1 end cell 1 end table close square brackets end cell end table 

 

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