Diketahui matriks [tex] A= \left[\begin{array}{ccc}-1&3\\5&2\end{array}\right] [/tex] dan [tex] A- B^{t} = (A+B)^{t}[/tex] . Jika [tex]C=\left[\begin{array}{ccc

[tex]B= \left[\begin{array}{ccc}a&b\\c&d\end{array}\right] ; A= \left[\begin{array}{ccc}-1&3\\5&2\end{array}\right] \\ \\ A-B^t=(A+B)^t \\ \\ \left[\begin{array}{ccc}-1&3\\5&2\end{array}\right] - \left[\begin{array}{ccc}a&c\\b&d\end{array}\right]=\left( \left[\begin{array}{ccc}-1&3\\5&2\end{array}\right] +\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\right)^t \\ \\ \left[\begin{array}{ccc}-1-a&3-c\\5-b&2-d\end{array}\right]= \left[\begin{array}{ccc}-1+a&3+b\\5+c&2+d\end{array}\right]^t[/tex]
[tex]\left[\begin{array}{ccc}-1-a&3-c\\5-b&2-d\end{array}\right]= \left[\begin{array}{ccc}-1+a&5+c\\3+b&2+d\end{array}\right] \\ \\ *)~-1-a=-1+a \\ ~~~~~~0=2a ~~~; a=0 \\ *)~3-c=5+c \\ ~~~~~~-2=2c~~~;c=-1 \\ *)~5-b=3+b \\ ~~~~~~2=2b~~~;b=1 \\ *)~2-d=2+d \\ ~~~~~~0=2d~~~;d=0[/tex]
Jadi,
[tex]B= \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] \\ \\ BC=\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] X\left[\begin{array}{ccc}5&1\\-3&4\end{array}\right] =\left[\begin{array}{ccc}-3&4\\-5&-1\end{array}\right] \\ \\ det (BC)= (-3)(-1)-(-5)(4)=3-(-20)=23 [/tex]
[A]