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Let

\begin{equation*} A = \begin{pmatrix} a \amp b \\ c \amp d \end{pmatrix}, x = \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}. \end{equation*}

This gives

\begin{equation*} b = \begin{pmatrix} x_1 a + x_2 b \\ x_1 c + x_2 d \end{pmatrix} = x_1 \begin{pmatrix} a \\ c \end{pmatrix} + x_2 \begin{pmatrix} b \\ d \end{pmatrix}. \end{equation*}

So \(b\) is a linear combination of the columns of \(A\) with coefficients from \(x\text{.}\)

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