Pertanyaan

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 $A = (12 - 1 k 21), B = (0131 2 - 1), (A B^{T})^{- 1} = (a c b d)$ dengan $B^{T}$ menyatakan transpose dari B. Jika det $(AB^{T}) = - 2$ , maka nilai a + b + c + d =….

-2
-1
0
1
2

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Pembahasan

Dicari terlebih dahulu : Sehingga

Dicari terlebih dahulu AB to the power of straight T :

Sehingga

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