Question

Consider the linear transformation T : R2 to R2
which rotates 60 degrees and refects with
respect to y-axis.
1. Find the matrix A of T in standard basis of R
2

Answer 1

\[A=\left[\begin{matrix}-1 & 0 \\ 0 & 1\end{matrix}\right]\left[\begin{matrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{matrix} \right]\]

The right matrix twists anticlockwise by theta radians, so just plug in pi/3. The left matrix reflects the first coordinate across the vertical axis.