Answer
The matrix T relative to $B$ and standard basis for $R^2$ is
$\begin{bmatrix}
2&-4&5\\
0&-1&3\\
\end{bmatrix}$
Work Step by Step
The matrix T relative to $B$ and standard basis for $R^2$ is
$\begin{bmatrix}
2&-4&5\\
0&-1&3\\
\end{bmatrix}$
$T(\vec{b_1})=[T(\vec{b_1})]_{R^2}=\begin{bmatrix}
2\\
0\\
\end{bmatrix}$
$T(\vec{b_2})=[T(\vec{b_2})]_{R^2}=\begin{bmatrix}
-4\\
-1\\
\end{bmatrix}$
$T(\vec{b_3})=[T(\vec{b_3})]_{R^2}=\begin{bmatrix}
5\\
3\\
\end{bmatrix}$
