Roboguru

Diketahui matriks  dan  Jika , dan maka nilai ...

Pertanyaan

Diketahui matriks A equals open square brackets table row cell 2 x plus 2 end cell 2 row cell negative 1 end cell cell 5 plus 2 y end cell end table close square brackets dan B equals open square brackets table row 4 cell negative 1 end cell row 2 9 end table close square brackets Jika straight B to the power of straight t equals transpos space matriks space straight B, dan A equals B to the power of t maka nilai x plus y equals ...

  1. 3space

  2. 4space

  3. 5space

  4. 6space

  5. 7space

Pembahasan Soal:

A equals open square brackets table row cell 2 x plus 2 end cell 2 row cell negative 1 end cell cell 5 plus 2 y end cell end table close square brackets

 B equals open square brackets table row 4 cell negative 1 end cell row 2 9 end table close square brackets, maka B to the power of t equals open square brackets table row 4 2 row cell negative 1 end cell 9 end table close square brackets

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell B to the power of t end cell row cell open square brackets table row cell 2 x plus 2 end cell 2 row cell negative 1 end cell cell 5 plus 2 y end cell end table close square brackets end cell equals cell open square brackets table row 4 2 row cell negative 1 end cell 9 end table close square brackets end cell end table

Sehingga didapat persamaan:

  table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 2 end cell equals 4 row cell 2 x end cell equals cell 4 minus 2 end cell row x equals cell 2 over 2 end cell row x equals 1 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 plus 2 y end cell equals 9 row cell 2 y end cell equals cell 9 minus 5 end cell row cell 2 y end cell equals 4 row y equals cell 4 over 2 end cell row y equals 2 end table

Maka, nilai  table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell 1 plus 2 end cell row blank equals 3 end table

Jadi, jawaban yang tepat adalah A

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Juni 2021

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