Exercise 5 — Linear Algebra

Let $T$ represent $t\colon\mathbb{C}^{2}\to\mathbb{C}^{2}$ with respect to $B,B$ .

T=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}\qquad B=\langle\begin{pmatrix}1\\ 0\end{pmatrix},\begin{pmatrix}1\\ 1\end{pmatrix}\rangle,\hskip 6.99997ptD=\langle\begin{pmatrix}2\\ 0\end{pmatrix},\begin{pmatrix}0\\ -2\end{pmatrix}\rangle

We will convert to the matrix representing $t$ with respect to $D,D$ .

Draw the arrow diagram.
Give the matrix that represents the left and right sides of that diagram, in the direction that we traverse the diagram to make the conversion.
Find ${\rm Rep}_{D,D}(t)$ .

AI Tutor