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Pertanyaan

Diberikan matriks begin mathsize 14px style A equals open parentheses table row 2 0 row 0 3 end table close parentheses space text dan end text space B equals open parentheses table row a b row 0 c end table close parentheses end style yang memenuhi persamaan matriks A B equals A plus B. Tentukan nilai open parentheses a times b times c close parentheses.space 

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai open parentheses a times b times c close parentheses adalah 0.space 

Pembahasan

Ingat kembali:

Jika matriks A equals open parentheses table row a b row c d end table close parentheses dan B equals open parentheses table row m n row o p end table close parentheses, maka

  • A B equals open parentheses table row a b row c d end table close parentheses open parentheses table row m n row o p end table close parentheses equals open parentheses table row cell a m plus b o end cell cell a n plus b p end cell row cell c m plus d o end cell cell c n plus d p end cell end table close parentheses
  • A plus B equals open parentheses table row a b row c d end table close parentheses plus open parentheses table row m n row o p end table close parentheses equals open parentheses table row cell a plus m end cell cell b plus n end cell row cell c plus o end cell cell d plus p end cell end table close parentheses
  • jika A equals B, maka a equals mb equals nc equals o, dan d equals p

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell A plus B end cell row cell open parentheses table row 2 0 row 0 3 end table close parentheses open parentheses table row a b row 0 c end table close parentheses end cell equals cell open parentheses table row 2 0 row 0 3 end table close parentheses plus open parentheses table row a b row 0 c end table close parentheses end cell row cell open parentheses table row cell 2 open parentheses a close parentheses plus 0 open parentheses 0 close parentheses end cell cell 2 open parentheses b close parentheses plus 0 open parentheses c close parentheses end cell row cell 0 open parentheses a close parentheses plus 3 open parentheses 0 close parentheses end cell cell 0 open parentheses b close parentheses plus 3 open parentheses c close parentheses end cell end table close parentheses end cell equals cell open parentheses table row cell 2 plus a end cell cell 0 plus b end cell row cell 0 plus 0 end cell cell 3 plus c end cell end table close parentheses end cell row cell open parentheses table row cell 2 a plus 0 end cell cell 2 b plus 0 end cell row cell 0 plus 0 end cell cell 0 plus 3 c end cell end table close parentheses end cell equals cell open parentheses table row cell 2 plus a end cell cell 0 plus b end cell row cell 0 plus 0 end cell cell 3 plus c end cell end table close parentheses end cell row cell open parentheses table row cell 2 a end cell cell 2 b end cell row 0 cell 3 c end cell end table close parentheses end cell equals cell open parentheses table row cell 2 plus a end cell b row 0 cell 3 plus c end cell end table close parentheses end cell end table

sehingga diperoleh

table row cell 2 a equals 2 plus a end cell blank cell midline horizontal ellipsis open parentheses 1 close parentheses end cell row cell 2 b equals b end cell blank cell midline horizontal ellipsis open parentheses 2 close parentheses end cell row cell 3 c equals 3 plus c end cell blank cell midline horizontal ellipsis open parentheses 3 close parentheses end cell end table

Dari open parentheses 1 close parentheses, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a end cell equals cell 2 plus a end cell row cell 2 a minus a end cell equals 2 row a equals 2 end table

Dari open parentheses 2 close parentheses, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b end cell equals b row cell 2 b minus b end cell equals 0 row b equals 0 end table

Dari open parentheses 3 close parentheses, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 c end cell equals cell 3 plus c end cell row cell 3 c minus c end cell equals 3 row cell 2 c end cell equals 3 row c equals cell 3 over 2 end cell end table

Oleh karena diperoleh a equals 2b equals 0, dan c equals 3 over 2, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a times b times c close parentheses end cell equals cell open parentheses 2 times 0 times 3 over 2 close parentheses end cell row blank equals 0 end table

Jadi, nilai open parentheses a times b times c close parentheses adalah 0.space 

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