Diketahui 3 buah matriks:  A=[13​24​], B=[x+y8​6y​], dan C=[914​1213​]  Jika B−A=Ct, tentukan nilai x dan y!

Pertanyaan

Diketahui 3 buah matriks: 

begin mathsize 14px style straight A equals open square brackets table row 1 2 row 3 4 end table close square brackets comma space straight B equals open square brackets table row cell straight x plus straight y end cell 6 row 8 straight y end table close square brackets comma space dan space straight C equals open square brackets table row 9 12 row 14 13 end table close square brackets end style 

Jika begin mathsize 14px style straight B minus straight A equals straight C to the power of straight t end style, tentukan nilai begin mathsize 14px style x space dan space y end style

  1. ...  

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style x equals negative 7 space dan space y equals 17 end style

Pembahasan

begin mathsize 14px style straight C equals open square brackets table row 9 12 row 14 13 end table close square brackets rightwards double arrow straight C to the power of straight t equals open square brackets table row 9 14 row 12 13 end table close square brackets end style 

dengan menggunkana kesamaan matriks diperoleh 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight B minus straight A end cell equals cell straight C to the power of straight t end cell row cell open square brackets table row cell x plus y end cell 6 row 8 y end table close square brackets minus open square brackets table row 1 2 row 3 4 end table close square brackets end cell equals cell open square brackets table row 9 14 row 12 13 end table close square brackets end cell row cell open square brackets table row cell x plus y minus 1 end cell 4 row 5 cell y minus 4 end cell end table close square brackets end cell equals cell open square brackets table row 9 14 row 12 13 end table close square brackets end cell row cell maka colon space y minus 4 end cell equals 13 row y equals 17 row blank blank blank row cell x plus y minus 1 end cell equals 9 row cell x plus 17 minus 1 end cell equals 9 row cell x plus 16 end cell equals 9 row x equals cell negative 7 end cell end table end style 

Jadi begin mathsize 14px style x equals negative 7 space dan space y equals 17 end style

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Diketahui matriks A=⎝⎛​ab−1​520​3c4​⎠⎞​ dan B=⎝⎛​253​2a2ab​−104​⎠⎞​, jika A=BT, dan BT adalah transpose matriks B, maka nilai a+b+c adalah ...

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