Consider the basis \mathcal{B} = \left\{ \begin{bmatrix} 1 \\3 \end{bmatrix} , \begin {bmatrix} 2 \\ -1 \end{bmatrix} ight\}. If \mathbf{x} = 7 \begin{bmatrix} 1 \\ 3 \end{bmatrix} + 4 \begin{bmatrix} 2 \\ -1 \end{bmatrix}, then the coordinate vector of \mathbf{x} relative to the basis \mathcal{B} is [\mathbf{x}]_{\mathcal{B}} = \begin{bmatrix} 7 \\ 4 \end{bmatrix}