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Jika maka adjoin dari matriks D adalah ....

Jika begin mathsize 14px style D equals open parentheses table row 1 0 3 row 2 2 cell negative 1 end cell row cell negative 1 end cell 3 5 end table close parentheses end style maka adjoin dari matriks D  adalah ....

  1. open parentheses table row 13 9 cell negative 6 end cell row cell negative 9 end cell 8 7 row 8 cell negative 3 end cell 2 end table close parentheses 

  2. begin mathsize 14px style open parentheses table row 13 cell negative 9 end cell 8 row cell negative 9 end cell 8 cell negative 3 end cell row cell negative 6 end cell 7 2 end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row cell negative 13 end cell 9 6 row 9 cell negative 8 end cell cell negative 7 end cell row cell negative 8 end cell 3 cell negative 2 end cell end table close parentheses end style 

  4. begin mathsize 14px style open parentheses table row cell negative 13 end cell 9 cell negative 8 end cell row 9 cell negative 8 end cell 3 row 6 cell negative 7 end cell cell negative 2 end cell end table close parentheses end style 

  5. begin mathsize 14px style open parentheses table row cell negative 13 end cell cell negative 9 end cell cell negative 8 end cell row 9 cell negative 8 end cell cell negative 7 end cell row 6 3 cell negative 2 end cell end table close parentheses end style 

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D. Riansyah

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Pembahasan

Diketahui . Adjoin dari matriks D diperoleh dari transpose matriks kofaktornya. Untuk menentukan kofaktornya, kita hitungdulu masing-masing nilai minornya. Sehingga kita peroleh matriks kofaktornya adalah Jadi, adjoinnya adalah

Diketahui undefined. 

 

Adjoin dari matriks D diperoleh dari transpose matriks kofaktornya. Untuk menentukan kofaktornya, kita hitung dulu masing-masing nilai minornya.

table attributes columnalign right center left columnspacing 0px end attributes row cell M subscript 11 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row 3 5 end table close vertical bar equals 2 times 5 minus open parentheses negative 1 close parentheses times 3 equals 10 plus 3 equals 13 end cell row cell C subscript 11 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 1 end exponent times M subscript 11 equals open parentheses negative 1 close parentheses squared times 13 equals 1 times 13 equals 13 end cell row cell M subscript 12 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row cell negative 1 end cell 5 end table close vertical bar equals 2 times 5 minus open parentheses negative 1 close parentheses times open parentheses negative 1 close parentheses equals 10 minus 1 equals 9 end cell row cell C subscript 12 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 2 end exponent times M subscript 12 equals open parentheses negative 1 close parentheses cubed times 9 equals open parentheses negative 1 close parentheses times 9 equals negative 9 end cell row cell M subscript 13 end cell equals cell open vertical bar table row 2 2 row cell negative 1 end cell 3 end table close vertical bar equals 2 times 3 minus 2 times open parentheses negative 1 close parentheses equals 6 plus 2 equals 8 end cell row cell C subscript 13 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 3 end exponent times M subscript 13 equals open parentheses negative 1 close parentheses to the power of 4 times 8 equals 1 times 8 equals 8 end cell row cell M subscript 21 end cell equals cell open vertical bar table row 0 3 row 3 5 end table close vertical bar equals 0 times 5 minus 3 times 3 equals 0 minus 9 equals negative 9 end cell row cell C subscript 21 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 1 end exponent times M subscript 21 equals open parentheses negative 1 close parentheses cubed times open parentheses negative 9 close parentheses equals open parentheses negative 1 close parentheses times open parentheses negative 9 close parentheses equals 9 end cell row cell M subscript 22 end cell equals cell open vertical bar table row 1 3 row cell negative 1 end cell 5 end table close vertical bar equals 1 times 5 minus 3 times open parentheses negative 1 close parentheses equals 5 plus 3 equals 8 end cell row cell C subscript 22 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 2 end exponent times M subscript 22 equals open parentheses negative 1 close parentheses to the power of 4 times 8 equals 1 times 8 equals 8 end cell row cell M subscript 23 end cell equals cell open vertical bar table row 1 0 row cell negative 1 end cell 3 end table close vertical bar equals 1 times 3 minus 0 times open parentheses negative 1 close parentheses equals 3 plus 0 equals 3 end cell row cell C subscript 23 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 3 end exponent times M subscript 23 equals open parentheses negative 1 close parentheses to the power of 5 times 3 equals open parentheses negative 1 close parentheses times 3 equals negative 3 end cell row cell M subscript 31 end cell equals cell open vertical bar table row 0 3 row 2 cell negative 1 end cell end table close vertical bar equals 0 times open parentheses negative 1 close parentheses minus 3 times 2 equals 0 minus 6 equals negative 6 end cell row cell C subscript 31 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 1 end exponent times M subscript 31 equals open parentheses negative 1 close parentheses to the power of 4 times open parentheses negative 6 close parentheses equals 1 times open parentheses negative 6 close parentheses equals negative 6 end cell row cell M subscript 32 end cell equals cell open vertical bar table row 1 3 row 2 cell negative 1 end cell end table close vertical bar equals 1 times open parentheses negative 1 close parentheses minus 3 times 2 equals negative 1 minus 6 equals negative 7 end cell row cell C subscript 32 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 2 end exponent times M subscript 32 equals open parentheses negative 1 close parentheses to the power of 5 times open parentheses negative 7 close parentheses equals open parentheses negative 1 close parentheses times open parentheses negative 7 close parentheses equals 7 end cell row cell M subscript 33 end cell equals cell open vertical bar table row 1 0 row 2 2 end table close vertical bar equals 1 times 2 minus 0 times 2 equals 2 minus 0 equals 2 end cell row cell C subscript 33 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 3 end exponent times M subscript 33 equals open parentheses negative 1 close parentheses to the power of 6 times 2 equals 1 times 2 equals 2 end cell row blank blank blank row blank blank blank row blank blank blank end table 

Sehingga kita peroleh matriks kofaktornya adalah

open parentheses table row 13 cell negative 9 end cell 8 row 9 8 cell negative 3 end cell row cell negative 6 end cell 7 2 end table close parentheses 

Jadi, adjoinnya adalah

open parentheses table row 13 cell negative 9 end cell 8 row 9 8 cell negative 3 end cell row cell negative 6 end cell 7 2 end table close parentheses to the power of T equals open parentheses table row 13 9 cell negative 6 end cell row cell negative 9 end cell 8 7 row 8 cell negative 3 end cell 2 end table close parentheses 

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