For a system of linear equations, \begin{align*} a_{11}x_1+a_{12}x_2+a_{13}x_3+\dots+a_{1n}x_n&=b_1\\ a_{21}x_1+a_{22}x_2+a_{23}x_3+\dots+a_{2n}x_n&=b_2\\ a_{31}x_1+a_{32}x_2+a_{33}x_3+\dots+a_{3n}x_n&=b_3\\ \vdots&\\ a_{m1}x_1+a_{m2}x_2+a_{m3}x_3+\dots+a_{mn}x_n&=b_m \end{align*} the solution vector is the column vector of size $n$ \begin{equation*} \vect{x}= \begin{bmatrix} x_1\\ x_2\\ x_3\\ \vdots\\ x_n\\ \end{bmatrix} \end{equation*}