For ordered bases $B,C$, $[v]_C=P_{C\leftarrow B}[v]_B$. For $B=((1,0),(1,1))$ and standard basis $E$, $P_{E\leftarrow B}=\begin{bmatrix}1&1\\0&1\end{bmatrix}$. Thus $[v]_B=(2,3)^T$ gives standard coordinates $(5,3)^T$. Always label the input and output bases to avoid reversing the conversion.
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