Exercise 3

Find the change of basis matrix for $B,D\subseteq\mathbb{R}^{2}$.

• (a)  $B={\cal E}_{2}$, $D=\langle\vec{e}_{2},\vec{e}_{1}\rangle$     (b)  $B={\cal E}_{2}$, $D=\langle\begin{pmatrix}1\\ 2\end{pmatrix},\begin{pmatrix}1\\ 4\end{pmatrix}\rangle$     (c)  $B=\langle\begin{pmatrix}1\\ 2\end{pmatrix},\begin{pmatrix}1\\ 4\end{pmatrix}\rangle$, $D={\cal E}_{2}$     (d)  $B=\langle\begin{pmatrix}-1\\ 1\end{pmatrix},\begin{pmatrix}2\\ 2\end{pmatrix}\rangle$, $D=\langle\begin{pmatrix}0\\ 4\end{pmatrix},\begin{pmatrix}1\\ 3\end{pmatrix}\rangle$