Solution: The matrix $\mathbf{M}$ is constructed by placing the images of the standard basis vectors as its columns. Thus, $\mathbf{M} = \begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix}$. Verifying, $\mathbf{M} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$ and $\mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$, confirming correctness. $\boxed{\begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix}}$

Tue, 05 May 2026 13:17:18 +0000

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