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# Definition of augmented matrix (of a linear system)

Put content here**Definition: Augmented Matrix**
⏎
The augmented matrix of a linear system is formed by appending the constant vector (right-hand side) as the last column of the coefficient matrix, separated by a vertical bar for clarity.
⏎
For the system `Ax = b` where `A` is `m × n`, the augmented matrix is `m × (n+1)`:
```
[a₁₁ a₁₂ ... a₁ₙ | b₁]
[a₂₁ a₂₂ ... a₂ₙ | b₂]
[...  ...  ... ... | ...]
[aₘ₁ aₘ₂ ... aₘₙ | bₘ]
```
⏎
**Example:** For the system:
```
2x + y - z = 8
-3x - y + 2z = -11
-2x + y + 2z = -3
```
⏎
The augmented matrix is:
```
[ 2  1 -1 |  8]
[-3 -1  2 |-11]
[-2  1  2 | -3]
```
⏎
The augmented matrix contains all the information needed to solve the system using row reduction.

# Parents

* Terminology