Pertanyaan

Diketahui A = [ 2 − 3 − 1 3 ] , C = [ 1 2 2 5 ] , dan D = [ 3 6 0 9 ] . Jika A ⋅ B ⋅ C = D maka matriks B adalah...

Diketahui $A = [2 - 3 - 1 3], C = [1225],$ dan $D = [3609] .$ Jika $A \cdot B \cdot C = D$ maka matriks B adalah... $\;$

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai matriks B adalah .

nilai matriks B adalah open square brackets table row 19 cell negative 7 end cell row 23 cell negative 8 end cell end table close square brackets

Pembahasan

Perhatikan penghitungan berikut! Jadi, nilai matriks B adalah .

Perhatikan penghitungan berikut!

$straight A times straight B times straight C equals straight D straight A to the power of negative 1 end exponent times straight A times straight B times straight C equals straight A to the power of negative 1 end exponent times straight D straight I times straight B times straight C equals straight A to the power of negative 1 end exponent times straight D straight B times straight C equals straight A to the power of negative 1 end exponent times straight D straight B times straight C times straight C to the power of negative 1 end exponent equals straight A to the power of negative 1 end exponent times straight D times straight C to the power of negative 1 end exponent straight B times straight I equals straight A to the power of negative 1 end exponent times straight D times straight C to the power of negative 1 end exponent straight B equals straight A to the power of negative 1 end exponent times straight D times straight C to the power of negative 1 end exponent straight A equals open square brackets table row 2 cell negative 1 end cell row cell negative 3 end cell 3 end table close square brackets space rightwards arrow straight A to the power of negative 1 end exponent equals fraction numerator 1 over denominator open parentheses 2 cross times 3 close parentheses minus open parentheses negative 1 cross times negative 3 close parentheses end fraction open square brackets table row 3 1 row 3 2 end table close square brackets straight A to the power of negative 1 end exponent equals 1 third open square brackets table row 3 1 row 3 2 end table close square brackets straight C equals open square brackets table row 1 2 row 2 5 end table close square brackets space rightwards arrow straight C to the power of negative 1 end exponent equals fraction numerator 1 over denominator open parentheses 1 cross times 5 close parentheses minus open parentheses 2 cross times 2 close parentheses end fraction open square brackets table row 5 cell negative 2 end cell row cell negative 2 end cell 1 end table close square brackets straight C to the power of negative 1 end exponent equals 1 over 1 open square brackets table row 5 cell negative 2 end cell row cell negative 2 end cell 1 end table close square brackets equals open square brackets table row 5 cell negative 2 end cell row cell negative 2 end cell 1 end table close square brackets straight B equals straight A to the power of negative 1 end exponent times straight D times straight C to the power of negative 1 end exponent straight B equals 1 third open square brackets table row 3 1 row 3 2 end table close square brackets times open square brackets table row 3 0 row 6 9 end table close square brackets times open square brackets table row 5 cell negative 2 end cell row cell negative 2 end cell 1 end table close square brackets straight B equals 1 third open square brackets table row 15 9 row 21 18 end table close square brackets times open square brackets table row 5 cell negative 2 end cell row cell negative 2 end cell 1 end table close square brackets straight B equals 1 third open square brackets table row 57 cell negative 21 end cell row 69 cell negative 24 end cell end table close square brackets straight B equals open square brackets table row 19 cell negative 7 end cell row 23 cell negative 8 end cell end table close square brackets$

Jadi, nilai matriks B adalah open square brackets table row 19 cell negative 7 end cell row 23 cell negative 8 end cell end table close square brackets . space space