Exercise 7 — Linear Algebra

Find the change of basis matrices $Q$ and $P$ that will convert the representation of a $t\colon\mathbb{R}^{2}\to\mathbb{R}^{2}$ with respect to $B,D$ to one with respect to $\hat{B},\hat{D}$ .

B=\langle\begin{pmatrix}1\\ 0\end{pmatrix},\begin{pmatrix}1\\ 1\end{pmatrix}\rangle\quad D=\langle\begin{pmatrix}0\\ 1\end{pmatrix},\begin{pmatrix}-1\\ 0\end{pmatrix}\rangle\quad\hat{B}={\cal E}_{2}\quad\hat{D}=\langle\begin{pmatrix}1\\ -1\end{pmatrix},\begin{pmatrix}0\\ 1\end{pmatrix}\rangle

Hefferon, Linear Algebra, Maps Between Spaces, Changing Map Representations, Exercise 7

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