I am given $T:\mathbb{R}^2\to \mathbb{R}^2$ a linear map that rotates the points throuh $-2\pi/3$ and then reflects the points through vertical $y$ axis.
So basically $T=T_1\circ T_2$, where $T_2$ is rotation and $T_1$ is reflection.
I know the rotation matrix is $\begin{pmatrix}\cos\theta & -\sin\theta\\\sin\theta &\cos \theta\end{pmatrix}$
so when $\theta =-2pi/3$ I will get $T_2$ matrix , now how will I get the final answer? Thanks
Best Answer
The matrix corresponding to $T_1$ is $\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}.$
You just have to compute $$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} $$