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Diketahui persamaan matriks sebagai berikut. (a−1​4c​)+(2d​b−3​)=(13​−34​)(−11​10​)  Nilai a−b+c−d=....

Pertanyaan

Diketahui persamaan matriks sebagai berikut.

open parentheses table row a 4 row cell negative 1 end cell c end table close parentheses plus open parentheses table row 2 b row d cell negative 3 end cell end table close parentheses equals open parentheses table row 1 cell negative 3 end cell row 3 4 end table close parentheses open parentheses table row cell negative 1 end cell 1 row 1 0 end table close parentheses 

Nilai a minus b plus c minus d equals.... 

  1. negative 7 

  2. negative 5 

  3. 1 

  4. 3 

  5. 7  

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Operasikan persamaan matriks tersebut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row a 4 row cell negative 1 end cell c end table close parentheses plus open parentheses table row 2 b row d cell negative 3 end cell end table close parentheses end cell equals cell open parentheses table row 1 cell negative 3 end cell row 3 4 end table close parentheses open parentheses table row cell negative 1 end cell 1 row 1 0 end table close parentheses end cell row cell open parentheses table row cell a plus 2 end cell cell 4 plus b end cell row cell negative 1 plus d end cell cell c minus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell 1 times open parentheses negative 1 close parentheses plus open parentheses negative 3 close parentheses times 1 end cell cell 1 times 1 plus open parentheses negative 3 close parentheses times 0 end cell row cell 3 times open parentheses negative 1 close parentheses plus 4 times 1 end cell cell 3 times 1 plus 4 times 0 end cell end table close parentheses end cell row cell open parentheses table row cell a plus 2 end cell cell 4 plus b end cell row cell negative 1 plus d end cell cell c minus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 1 minus 3 end cell cell 1 plus 0 end cell row cell negative 3 plus 4 end cell cell 3 plus 0 end cell end table close parentheses end cell row cell open parentheses table row cell a plus 2 end cell cell 4 plus b end cell row cell negative 1 plus d end cell cell c minus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 4 end cell 1 row 1 3 end table close parentheses end cell end table end style  

Berdasarkan kesamaan matriks di atas, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 2 end cell equals cell negative 4 end cell row cell a plus 2 minus 2 end cell equals cell negative 4 minus 2 end cell row cell therefore space a end cell equals cell negative 6 end cell end table 
 

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 plus b end cell equals 1 row cell 4 plus b minus 4 end cell equals cell 1 minus 4 end cell row cell therefore space b end cell equals cell negative 3 end cell end table 
 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 plus d end cell equals 1 row cell negative 1 plus d plus 1 end cell equals cell 1 plus 1 end cell row cell therefore space d end cell equals 2 end table 
 

table attributes columnalign right center left columnspacing 0px end attributes row cell c minus 3 end cell equals 3 row cell c minus 3 plus 3 end cell equals cell 3 plus 3 end cell row cell therefore space c end cell equals 6 end table   

Sehingga, nilai a minus b plus c minus d equals negative 6 minus open parentheses negative 3 close parentheses plus 6 minus 2 equals 1  

Jadi, jawaban yang tepat adalah C.

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