Exercise 4

Suppose that, with respect to

the transformation $t\colon\mathbb{R}^{2}\to\mathbb{R}^{2}$ is represented by this matrix.

Use change of basis matrices to represent $t$ with respect to each pair.

• $\hat{B}=\langle\begin{pmatrix}0\\ 1\end{pmatrix},\begin{pmatrix}1\\ 1\end{pmatrix}\rangle$, $\hat{D}=\langle\begin{pmatrix}-1\\ 0\end{pmatrix},\begin{pmatrix}2\\ 1\end{pmatrix}\rangle$

• $\hat{B}=\langle\begin{pmatrix}1\\ 2\end{pmatrix},\begin{pmatrix}1\\ 0\end{pmatrix}\rangle$, $\hat{D}=\langle\begin{pmatrix}1\\ 2\end{pmatrix},\begin{pmatrix}2\\ 1\end{pmatrix}\rangle$