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Diketahui A = ( 1 2 ​ − 1 k ​ 2 1 ​ ) , B = ( 0 1 ​ 3 1 ​ 2 − 1 ​ ) , ( A B T ) − 1 = ( a c ​ b d ​ ) dengan B T menyatakan transpose dari B. Jika det ( AB T ) = − 2 , maka nilai a + b + c + d =….

Diketahui  dengan menyatakan transpose dari B. Jika det , maka nilai a + b + c + d =….

  1. -2

  2. -1

  3. 0

  4. 1

  5. 2

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Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

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Pembahasan

Dicari terlebih dahulu : Sehingga

Dicari terlebih dahulu AB to the power of straight T:

AB to the power of straight T equals open parentheses table row 1 cell negative 1 end cell 2 row 2 straight k 1 end table close parentheses open parentheses table row 0 1 row 3 1 row 2 cell negative 1 end cell end table close parentheses equals open parentheses table row 1 cell negative 2 end cell row cell 3 straight k plus 2 end cell cell straight k plus 1 end cell end table close parentheses det space left parenthesis AB to the power of straight T right parenthesis equals 1. open parentheses straight k plus 1 close parentheses minus open parentheses negative 2 close parentheses. open parentheses 3 straight k plus 2 close parentheses space space space space space space space space space minus 2 space space equals straight k plus 1 plus 6 straight k plus 4 space space space space space space space space space minus 2 equals 7 straight k plus 5 rightwards arrow straight k equals negative 1

Sehingga

AB to the power of straight T equals open parentheses table row 1 cell negative 2 end cell row cell 3 left parenthesis negative 1 right parenthesis plus 2 end cell cell left parenthesis negative 1 right parenthesis plus 1 end cell end table close parentheses equals open parentheses table row 1 cell negative 2 end cell row cell negative 1 end cell 0 end table close parentheses rightwards arrow open parentheses AB to the power of straight T close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator 1.0 minus left parenthesis negative 2 right parenthesis left parenthesis negative 1 right parenthesis end fraction open parentheses table row 0 2 row 1 1 end table close parentheses equals open parentheses table row 0 cell negative 1 end cell row cell negative 1 half end cell cell negative 1 half end cell end table close parentheses Karena space open parentheses AB to the power of straight T close parentheses to the power of negative 1 end exponent equals open parentheses table row straight a straight b row straight c straight d end table close parentheses equals open parentheses table row 0 cell negative 1 end cell row cell negative 1 half end cell cell negative 1 half end cell end table close parentheses Maka space straight a plus straight b plus straight c plus straight d equals 0 minus 1 minus 1 half minus 1 half equals negative 2

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