Linear System = System of Linear Equations

standard (unit) vector

only one element is "1", the rest elements are "0"

$v = \begin{bmatrix} v_1 \\ v_2\end{bmatrix} = v_1\begin{bmatrix} 1 \\ 0\end{bmatrix} + v_2\begin{bmatrix} 0 \\ 1\end{bmatrix} = v_1e_1 + v_2e_2$