Pertanyaan

Jika matriks B memenuhi persamaan: B . ( 3 1 2 − 1 ) = ( 2 1 1 3 ) , maka determinan matriks adalah ...

Jika matriks $B$ memenuhi persamaan:

$B . (31 2 - 1) = (2113),$

maka determinan matriks adalah ...

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Diketahui maka: Sehingga: Jadi, jawaban yang tepat adalah A.

Diketahui B. open parentheses table row 3 2 row 1 cell negative 1 end cell end table close parentheses equals open parentheses table row 2 1 row 1 3 end table close parentheses comma maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell size 12px B size 12px. size 12px I end cell size 12px equals cell begin mathsize 12px style open parentheses table row 2 1 row 1 3 end table close parentheses end style size 12px. fraction numerator size 12px 1 over denominator size 12px minus size 12px 3 size 12px minus size 12px 2 end fraction begin mathsize 12px style open parentheses table row 3 2 row 1 cell negative 1 end cell end table close parentheses end style end cell row size 12px B size 12px equals cell size 12px minus size 12px 1 over size 12px 5 size 12px. begin mathsize 12px style open parentheses table row 2 1 row 1 3 end table close parentheses end style size 12px. begin mathsize 12px style open parentheses table row 3 2 row 1 cell negative 1 end cell end table close parentheses end style end cell row size 12px B size 12px equals cell size 12px minus size 12px 1 over size 12px 5 size 12px. begin mathsize 12px style open parentheses table row cell 2 cross times 3 plus 1 cross times 1 end cell cell 2 cross times 2 plus 1 cross times left parenthesis negative 1 right parenthesis end cell row cell 1 cross times 3 plus 3 cross times 1 end cell cell 1 cross times 2 plus 3 cross times left parenthesis negative 1 right parenthesis end cell end table close parentheses end style end cell row size 12px B size 12px equals cell size 12px minus size 12px 1 over size 12px 5 size 12px. begin mathsize 12px style open parentheses table row 7 3 row 6 cell negative 1 end cell end table close parentheses end style end cell row size 12px B size 12px equals cell begin mathsize 12px style open parentheses table row cell bevelled fraction numerator negative 7 over denominator 5 end fraction end cell cell bevelled fraction numerator negative 3 over denominator 5 end fraction end cell row cell bevelled fraction numerator negative 6 over denominator 5 end fraction end cell cell bevelled 1 fifth end cell end table close parentheses end style end cell end table$

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell det space B end cell equals cell negative 7 over 5 cross times 1 fifth minus open parentheses negative 6 over 5 cross times open parentheses negative 3 over 5 close parentheses close parentheses end cell row blank equals cell negative 7 over 25 minus 18 over 25 end cell row blank equals cell fraction numerator negative 25 over denominator 25 end fraction end cell row blank equals cell negative 1 end cell end table$

Jadi, jawaban yang tepat adalah A.