\begin{definition}[Definition:Augmented Matrix]
Let $\mathbf A$ be a matrix of order $n \times m$.
Let $\mathbf B$ be a matrix of order $n \times k$.
The '''augmented matrix''' of $\mathbf A$ and $\mathbf B$ is the block matrix $\begin {pmatrix} \mathbf A & \mathbf B \end {pmatrix}$ of order $n \times \paren {m + k}$.
\end{definition}