\mathbf{M} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
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- Question: Find the matrix $\mathbf{M}$ such that
- \mathbf{M} \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}, \quad \mathbf{M} \begin{pmatrix} 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}
- Let
- Apply the first condition:
- \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} a + 2b \\ c + 2d \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}
- \Rightarrow a + 2b = 3, \quad c + 2d = 4
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