# Definition:Augmented Matrix

## Definition

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 $n \times \paren {m + k}$.

### Augmented Matrix of Simultaneous Equations

Let $\begin {bmatrix} \mathbf A & \mathbf b \end {bmatrix}$ be the block matrix formed from $\mathbf A$ and $\mathbf b$.

Then $\begin {bmatrix} \mathbf A & \mathbf b \end {bmatrix}$ is known as the augmented matrix of the system.