Diketahui matriks K=[a0​b1​], L=[6−8​17​], M=[21​−2c​], N=[10​−12​]. Jika 2K+LT=MN. Nilai a+b−2c adalah...

Pertanyaan

Diketahui matriks K equals open square brackets table row a b row 0 1 end table close square brackets comma space L equals open square brackets table row 6 1 row cell negative 8 end cell 7 end table close square brackets comma space M equals open square brackets table row 2 cell negative 2 end cell row 1 c end table close square brackets comma space N equals open square brackets table row 1 cell negative 1 end cell row 0 2 end table close square brackets. Jika 2 K plus L to the power of T equals M N. Nilai a plus b minus 2 c adalah... 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

nilai dari a plus b minus 2 c equals negative 11.

Pembahasan

Diketahui bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 K plus L to the power of T end cell equals cell M N end cell row cell 2 open square brackets table row a b row 0 1 end table close square brackets plus open square brackets table row 6 1 row cell negative 8 end cell 7 end table close square brackets to the power of T end cell equals cell open square brackets table row 2 cell negative 2 end cell row 1 c end table close square brackets open square brackets table row 1 cell negative 1 end cell row 0 2 end table close square brackets end cell row cell open square brackets table row cell 2 a end cell cell 2 b end cell row 0 2 end table close square brackets plus open square brackets table row 6 cell negative 8 end cell row 1 7 end table close square brackets end cell equals cell open square brackets table row cell 2 times 1 plus left parenthesis negative 2 right parenthesis times 0 end cell cell 2 times left parenthesis negative 1 right parenthesis plus left parenthesis negative 2 right parenthesis times 2 end cell row cell 1 times 1 plus c times 0 end cell cell 1 times left parenthesis negative 1 right parenthesis plus c times 2 end cell end table close square brackets end cell row cell open square brackets table row cell 2 a plus 6 end cell cell 2 b minus 8 end cell row 1 9 end table close square brackets end cell equals cell open square brackets table row 2 cell negative 6 end cell row 1 cell 2 c minus 1 end cell end table close square brackets end cell end table  

Berdasarkan kesamaan matriks, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a plus 6 end cell equals 2 row cell 2 a end cell equals cell 2 minus 6 end cell row cell 2 a end cell equals cell negative 4 end cell row a equals cell fraction numerator negative 4 over denominator 2 end fraction end cell row a equals cell negative 2 end cell end table 

dan 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b minus 8 end cell equals cell negative 6 end cell row cell 2 b end cell equals cell negative 6 plus 8 end cell row cell 2 b end cell equals 2 row b equals cell 2 over 2 end cell row b equals 1 end table 

dan 

table attributes columnalign right center left columnspacing 0px end attributes row 9 equals cell 2 c minus 1 end cell row cell 9 plus 1 end cell equals cell 2 c end cell row 10 equals cell 2 c end cell row cell 10 over 2 end cell equals c row 5 equals c end table 

Nilai a plus b minus 2 c adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a plus b minus 2 c end cell row blank equals cell negative 2 plus 1 minus 2 left parenthesis 5 right parenthesis end cell row blank equals cell negative 1 minus 10 end cell row blank equals cell negative 11 end cell end table 

Jadi, nilai dari a plus b minus 2 c equals negative 11.

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