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Pertanyaan

Diketahui A equals open parentheses table row cell a plus b end cell cell negative c end cell row b cell a minus b end cell end table close parentheses  matriks B equals open parentheses table row 1 a row cell 3 b end cell c end table close parentheses, dan C equals open parentheses table row cell negative 3 end cell 0 row cell 5 b end cell cell negative a end cell end table close parentheses. Jika B plus C equals negative 2 A to the power of T dengan A to the power of T adalah transpose A, maka nilai left parenthesis a plus b plus c right parenthesis adalah ...

  1. negative 5

  2. negative 3

  3. negative 1

  4. 3

  5. 5

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Diketahui A equals open parentheses table row cell a plus b end cell cell negative c end cell row b cell a minus b end cell end table close parentheses, maka A to the power of T equals open parentheses table row cell a plus b end cell b row cell negative c end cell cell a minus b end cell end table close parentheses, matriks B equals open parentheses table row 1 a row cell 3 b end cell c end table close parentheses, dan C equals open parentheses table row cell negative 3 end cell 0 row cell 5 b end cell cell negative a end cell end table close parentheses. Jika B plus C equals negative 2 A to the power of T, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell B plus C end cell equals cell negative 2 A to the power of T end cell row cell open parentheses table row 1 a row cell 3 b end cell c end table close parentheses plus open parentheses table row cell negative 3 end cell 0 row cell 5 b end cell cell negative a end cell end table close parentheses end cell equals cell negative 2 cross times open parentheses table row cell a plus b end cell b row cell negative c end cell cell a minus b end cell end table close parentheses end cell row cell open parentheses table row cell 1 plus left parenthesis negative 3 right parenthesis end cell cell a plus 0 end cell row cell 3 b plus 5 b end cell cell c plus left parenthesis negative a right parenthesis end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 a minus 2 b end cell cell negative 2 b end cell row cell 2 c end cell cell negative 2 a plus 2 b end cell end table close parentheses end cell row cell open parentheses table row cell negative 2 end cell a row cell 8 b end cell cell c minus a end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 a minus 2 b end cell cell negative 2 b end cell row cell 2 c end cell cell negative 2 a plus 2 b end cell end table close parentheses end cell end table

Dari kesamaan diatas, didapat a equals negative 2 b, 8 b equals 2 c dan negative 2 equals negative 2 a minus 2 b, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 end cell equals cell negative 2 a minus 2 b end cell row cell negative 2 end cell equals cell negative 2 left parenthesis negative 2 b right parenthesis minus 2 b end cell row cell negative 2 end cell equals cell 4 b minus 2 b end cell row cell negative 2 end cell equals cell 2 b end cell row b equals cell fraction numerator negative 2 over denominator 2 end fraction end cell row b equals cell negative 1 end cell row blank blank blank row a equals cell negative 2 b end cell row blank equals cell negative 2 left parenthesis negative 1 right parenthesis end cell row blank equals 2 row blank blank blank row cell 8 b end cell equals cell 2 c end cell row cell 8 left parenthesis negative 1 right parenthesis end cell equals cell 2 c end cell row cell negative 8 end cell equals cell 2 c end cell row c equals cell fraction numerator negative 8 over denominator 2 end fraction end cell row c equals cell negative 4 end cell end table  

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b plus c end cell equals cell 2 plus left parenthesis negative 1 right parenthesis plus left parenthesis negative 4 right parenthesis end cell row blank equals cell negative 3 end cell end table 

Jadi, jawaban yang tepat adalah B

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