Editing System of linear equations (section)

===Matrix equation===
The vector equation is equivalent to a [[matrix (mathematics)|matrix]] equation of the form
<math display="block"> A\mathbf{x} = \mathbf{b} </math>
where ''A'' is an ''m''×''n'' matrix, '''x''' is a [[column vector]] with ''n'' entries, and '''b''' is a column vector with ''m'' entries.{{sfnp|Beauregard| Fraleigh|1973|pp=65&ndash;66}}

<math display="block">
A=
\begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{bmatrix},\quad
\mathbf{x}=
\begin{bmatrix}
x_1 \\
x_2 \\
\vdots \\
x_n
\end{bmatrix},\quad
\mathbf{b}=
\begin{bmatrix}
b_1 \\
b_2 \\
\vdots \\
b_m
\end{bmatrix}.
</math>
The number of vectors in a basis for the span is now expressed as the ''[[rank (linear algebra)|rank]]'' of the matrix.