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Tentukan determinan dan adjoin dari matriks berikut. d.

Pertanyaan

Tentukan determinan dan adjoin dari matriks berikut.

d. begin mathsize 14px style straight D equals open parentheses table row 1 cell negative 2 end cell cell negative 1 end cell row 0 5 0 row 4 0 cell negative 2 end cell end table close parentheses end style      undefined      space undefined 

Pembahasan Soal:

Perhatikan penghitungan berikut!

begin mathsize 14px style straight D equals open parentheses table row 1 cell negative 2 end cell cell negative 1 end cell row 0 5 0 row 4 0 cell negative 2 end cell end table close parentheses table row 1 cell negative 2 end cell row 0 5 row 4 0 end table det left parenthesis straight D right parenthesis equals open parentheses negative 10 plus 0 plus 0 close parentheses minus left parenthesis negative 20 plus 0 plus 0 right parenthesis det left parenthesis straight D right parenthesis equals 10  matriks space adjoin space straight D a subscript 11 equals open parentheses negative 1 close parentheses to the power of 1 plus 1 end exponent space open vertical bar table row 5 0 row 0 cell negative 2 end cell end table close vertical bar equals negative 10 a subscript 12 equals open parentheses negative 1 close parentheses to the power of 1 plus 2 end exponent space open vertical bar table row 0 0 row 4 cell negative 2 end cell end table close vertical bar equals 0 a subscript 13 equals open parentheses negative 1 close parentheses to the power of 1 plus 3 end exponent space open vertical bar table row 0 5 row 4 0 end table close vertical bar equals negative 20 a subscript 21 equals open parentheses negative 1 close parentheses to the power of 2 plus 1 end exponent space open vertical bar table row cell negative 2 end cell cell negative 1 end cell row 0 cell negative 2 end cell end table close vertical bar equals negative 4 a subscript 22 equals open parentheses negative 1 close parentheses to the power of 2 plus 2 end exponent space open vertical bar table row 1 cell negative 1 end cell row 4 cell negative 2 end cell end table close vertical bar equals 2 a subscript 23 equals open parentheses negative 1 close parentheses to the power of 2 plus 3 end exponent space open vertical bar table row 1 cell negative 2 end cell row 4 0 end table close vertical bar equals negative 8 a subscript 31 equals open parentheses negative 1 close parentheses to the power of 3 plus 1 end exponent space open vertical bar table row cell negative 2 end cell cell negative 1 end cell row 5 0 end table close vertical bar equals 5 a subscript 32 equals open parentheses negative 1 close parentheses to the power of 3 plus 2 end exponent space open vertical bar table row 1 cell negative 1 end cell row 0 0 end table close vertical bar equals 0 a subscript 33 equals open parentheses negative 1 close parentheses to the power of 3 plus 3 end exponent space open vertical bar table row 1 cell negative 2 end cell row 0 5 end table close vertical bar equals 5 adj left parenthesis straight D right parenthesis equals open parentheses table row cell negative 10 end cell 0 cell negative 20 end cell row cell negative 4 end cell 2 cell negative 8 end cell row 5 0 5 end table close parentheses end style 

Jadi, determinan matriks D adalah 10 dan matriks adjoin D adalah begin mathsize 14px style adj left parenthesis straight D right parenthesis equals open parentheses table row cell negative 10 end cell 0 cell negative 20 end cell row cell negative 4 end cell 2 cell negative 8 end cell row 5 0 5 end table close parentheses. end style 

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Terakhir diupdate 12 Maret 2021

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