Pertanyaan

Diketahui matriks A = ( − 4 4 − 2 p ) , B = ( − 1 3 8 − 4 ) , dan C = ( − 2 14 − 24 8 ) . Jika A B = C , nilai p = ...

Diketahui matriks $A = (- 4 4 - 2 p)$ , $B = (- 1 3 8 - 4)$ , dan $C = (- 2 14 - 24 8)$ . Jika $A B = C$ , nilai $p =$ ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Persamaan matriks bentuk berlaku: Sehingga diperoleh penyelesaiannya yaitu: Nilai . Oleh karena itu, jawaban yang benar adalah E.

Persamaan matriks bentuk X A equals B berlaku:

Sehingga diperoleh penyelesaiannya yaitu:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals C row cell open parentheses table row cell negative 4 end cell cell negative 2 end cell row 4 p end table close parentheses open parentheses table row cell negative 1 end cell 8 row 3 cell negative 4 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses end cell row cell open parentheses table row cell negative 4 end cell cell negative 2 end cell row 4 p end table close parentheses end cell equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses open parentheses table row cell negative 1 end cell 8 row 3 cell negative 4 end cell end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses times fraction numerator 1 over denominator negative 1 open parentheses negative 4 close parentheses minus 8 open parentheses 3 close parentheses end fraction open parentheses table row cell negative 4 end cell cell negative 8 end cell row cell negative 3 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses times fraction numerator 1 over denominator 4 minus 24 end fraction open parentheses table row cell negative 4 end cell cell negative 8 end cell row cell negative 3 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses times open parentheses negative 1 over 20 close parentheses open parentheses table row cell negative 4 end cell cell negative 8 end cell row cell negative 3 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses open parentheses table row cell fraction numerator negative 4 over denominator negative 20 end fraction end cell cell fraction numerator negative 8 over denominator negative 20 end fraction end cell row cell fraction numerator negative 3 over denominator negative 20 end fraction end cell cell fraction numerator negative 1 over denominator negative 20 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell cell negative 24 end cell row 14 8 end table close parentheses open parentheses table row cell 1 fifth end cell cell 2 over 5 end cell row cell 3 over 20 end cell cell 1 over 20 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 open parentheses 1 fifth close parentheses plus open parentheses negative 24 close parentheses open parentheses 3 over 20 close parentheses end cell cell negative 2 open parentheses 2 over 5 close parentheses plus open parentheses negative 24 close parentheses open parentheses 1 over 20 close parentheses end cell row cell 14 open parentheses 1 fifth close parentheses plus 8 open parentheses 3 over 20 close parentheses end cell cell 14 open parentheses 2 over 5 close parentheses plus 8 open parentheses 1 over 20 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 over 5 minus 18 over 5 end cell cell negative 4 over 5 minus 6 over 5 end cell row cell 14 over 5 plus 6 over 5 end cell cell 28 over 5 plus 2 over 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 20 over 5 end cell cell negative 10 over 5 end cell row cell 20 over 5 end cell cell 30 over 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell cell negative 2 end cell row 4 6 end table close parentheses end cell end table end style$

Nilai p equals .

Oleh karena itu, jawaban yang benar adalah E.