Pertanyaan

Jika P = [ 2 1 3 0 ] dan Q = [ − 4 3 − 3 3 ] maka ( PQ ) − 1 adalah ....

Jika $P = [2130]$ dan $Q = [- 4 3 - 3 3]$ maka $(PQ)^{- 1}$ adalah ....

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Habis dalam

Klaim

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

adalah .

left parenthesis P Q right parenthesis to the power of negative 1 end exponent

adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell negative 1 third end cell cell negative 1 third end cell row cell 4 over 9 end cell cell 1 over 9 end cell end table close square brackets end cell end table

Pembahasan

Dengan menggunakan konsep perkalian matriks dan invers matriks, maka didapatkan: Jadi, adalah .

Dengan menggunakan konsep perkalian matriks dan invers matriks, maka didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell P Q end cell equals cell open square brackets table row 2 3 row 1 0 end table close square brackets open square brackets table row cell negative 4 end cell cell negative 3 end cell row 3 3 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 8 plus 9 end cell cell negative 6 plus 9 end cell row cell negative 4 plus 0 end cell cell negative 3 plus 0 end cell end table close square brackets end cell row blank equals cell open square brackets table row 1 3 row cell negative 4 end cell cell negative 3 end cell end table close square brackets end cell row blank blank blank row cell open parentheses P Q close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 1 times open parentheses negative 3 close parentheses minus open parentheses 3 times open parentheses negative 4 close parentheses close parentheses end fraction open square brackets table row cell negative 3 end cell cell negative 3 end cell row 4 1 end table close square brackets end cell row blank equals cell 1 over 9 open square brackets table row cell negative 3 end cell cell negative 3 end cell row 4 1 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 1 third end cell cell negative 1 third end cell row cell 4 over 9 end cell cell 1 over 9 end cell end table close square brackets end cell end table$

Jadi, left parenthesis P Q right parenthesis to the power of negative 1 end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row cell negative 1 third end cell cell negative 1 third end cell row cell 4 over 9 end cell cell 1 over 9 end cell end table close square brackets end cell end table .