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Tentukan: b. Determinan Matriks G Transpose

begin mathsize 14px style straight G equals open square brackets table row 3 4 0 row 2 5 cell negative 1 end cell row 1 0 1 end table close square brackets comma space straight F equals open square brackets table row 2 2 row 4 0 end table close square brackets comma space straight K equals open square brackets table row cell negative 3 end cell 0 row 4 2 end table close square brackets end style 

Tentukan:

b. Determinan Matriks G Transpose

Jawaban:

Diketahui: 

begin mathsize 14px style straight G equals open square brackets table row 3 4 0 row 2 5 cell negative 1 end cell row 1 0 1 end table close square brackets end style 

Maka:

begin mathsize 14px style straight G equals open square brackets table row 3 4 0 row 2 5 cell negative 1 end cell row 1 0 1 end table close square brackets rightwards arrow straight G to the power of straight T equals open square brackets table row 3 2 1 row 4 5 0 row 0 cell negative 1 end cell 1 end table close square brackets left enclose table row 3 row 4 row 0 end table table row 2 row 5 row cell negative 1 end cell end table end enclose det. space straight G to the power of straight T equals open square brackets open parentheses 3 times 5 times 1 close parentheses plus open parentheses 2 times 0 times 0 close parentheses plus open parentheses 1 times 4 times negative 1 close parentheses close square brackets minus open square brackets open parentheses 1 times 5 times 0 close parentheses plus open parentheses 3 times 0 times negative 1 close parentheses plus open parentheses 2 times 4 times 1 close parentheses close square brackets det. space straight G to the power of straight T equals open square brackets open parentheses 15 close parentheses plus open parentheses 0 close parentheses plus open parentheses negative 4 close parentheses close square brackets minus open square brackets open parentheses 0 close parentheses plus open parentheses 0 close parentheses plus open parentheses 8 close parentheses close square brackets det. space straight G to the power of straight T equals open square brackets 15 minus 4 close square brackets minus open square brackets 8 close square brackets det. space straight G to the power of straight T equals 11 minus 8 det. space straight G to the power of straight T equals 3 end style  

Jadi, determinan matriks G Transpose adalah begin mathsize 14px style 3 end style.

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