Transformasi T mewakili dilatasi [O,2], dilanjutkan refleksi terhadap garus y = x, dan dilanjutkan rotasu R[O, -1/2π]. a. Nyatakan T sebagai transformasi tungg

jawab
T1  = D[O,2]
[tex]T_1\,=\, \left[\begin{array}{ccc}2&0\\0&2\end{array}\right] [/tex]

T2  = R(y = x)
[tex]T_2\,=\, \left[\begin{array}{ccc}0&1\\1&0\end{array}\right] [/tex]

T3 =  R[ O, -1/2π] = R[O, -90]
[tex]T_3\,=\, \left[\begin{array}{ccc}cos\,(-90)&-sin\,(-90)\\-sin\,(-90)&cos\,(-90)\end{array}\right]\,=\, \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] [/tex]

a) Matriks transformasi tunggal T4 = T3 o T2 o T1
[tex]T_4\,=\, \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\,\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]\,\left[\begin{array}{ccc}2&0\\0&2\end{array}\right] [/tex]

[tex]T_4\,=\,\left[\begin{array}{ccc}2&0\\0&-2\end{array}\right] [/tex]

b) [T4] [A]  = [A']
A = [T4]⁻¹ [ A ' ]

[tex]A\,=\, \frac{1}{2(-2)-0} \left[\begin{array}{ccc}-2&0\\0&2\end{array}\right]\, \left[\begin{array}{ccc}12\\-8\end{array}\right] [/tex]

[tex]A\,=\, \frac{1}{-4} \, \left[\begin{array}{ccc}24\\-16\end{array}\right][/tex]

A = ( 6, 4 )