Jawab:
A' = (9,-18)
Penjelasan dengan langkah-langkah:
[tex]\bold{A} = \left[\begin{array}{ccc}3\\ 4\\ \end{array}\right] \to \bold{A}= \left[\begin{array}{ccc}3\\ 4\\ 1\end{array}\right] , \bold{T} = \left[\begin{array}{ccc}1&0&1\\0&1&-2\\0&0&1\end{array}\right] , \bold{T'}=\left[\begin{array}{ccc}1&0&-1\\0&1&2\\0&0&1\end{array}\right] \\[/tex]
[tex]\bold{R} = \left[\begin{array}{ccc}\cos(90^{\circ})&-\sin(90^{\circ})&0\\\sin(90^{\circ})&\cos(90^{\circ}) &0\\0&0&1\end{array}\right] = \left[\begin{array}{ccc}0&-1&0\\1&0&0\\0&0&1\end{array}\right] \\\bold{S} = \left[\begin{array}{ccc}-3&0&0\\0&-3&0\\0&0&1\end{array}\right][/tex]
[tex]\bold{A'} = \bold{S\cdot T'\cdot R\cdot T\cdot A}\\\\ \bold{A'} = \left[\begin{array}{ccc}-3&0&0\\0&-3&0\\0&0&1\end{array}\right] \cdot \left[\begin{array}{ccc}1&0&-1\\0&1&2\\0&0&1\end{array}\right] \cdot \left[\begin{array}{ccc}0&-1&0\\1&0&0\\0&0&1\end{array}\right] \cdot \left[\begin{array}{ccc}1&0&1\\0&1&-2\\0&0&1\end{array}\right] \cdot \left[\begin{array}{ccc}3\\ 4\\ 1\end{array}\right][/tex]
[tex]\bold{A'} = \left[\begin{array}{ccc}-3&0&3\\0&-3&-6\\0&0&1\end{array}\right] \cdot \left[\begin{array}{ccc}0&-1&2\\1&0&1\\0&0&1\end{array}\right]\cdot \left[\begin{array}{ccc}3\\ 4\\ 1\end{array}\right]\\ \bold{A'} = \left[\begin{array}{ccc}0&3&-3\\-3&0&-9\\0&0&1\end{array}\right]\cdot \left[\begin{array}{ccc}3\\ 4\\ 1\end{array}\right]\\ \bold{A'} = \left[\begin{array}{ccc}0+12-3\\ -9+0-9\\ 0+0+1\end{array}\right] = \left[\begin{array}{ccc}9\\ -18\\ 1\end{array}\right][/tex]
[tex]\Huge{\boxed{\boxed{\boldsymbol{{\bold{A'} = \left[\begin{array}{ccc}9\\ -18\\ \end{array}\right]\\}}}}[/tex]
[answer.2.content]
