# Example of solving a 3-by-3 matrix equation

Put content here.## Example: Solving a 3-by-3 Matrix Equation
⏎
Solve `Ax = b` where:
```
A = [ 1  2 -1]    b = [ 8]
    [-3 -1  2]        [-11]
    [-2  1  2]        [ -3]
```
⏎
**Step 1:** Form the augmented matrix `[A | b]`
```
[ 1  2 -1 |  8]
[-3 -1  2 |-11]
[-2  1  2 | -3]
```
⏎
**Step 2:** R₂ → R₂ + 3R₁, R₃ → R₃ + 2R₁
```
[ 1  2 -1 |  8 ]
[ 0  5 -1 | 13 ]
[ 0  5  0 | 13 ]
```
⏎
**Step 3:** R₃ → R₃ - R₂
```
[ 1  2 -1 |  8 ]
[ 0  5 -1 | 13 ]
[ 0  0  1 |  0 ]
```
⏎
**Step 4:** From R₃: z = 0. From R₂: 5y = 13, so y = 13/5. Wait -- let me redo with integer-friendly steps.
⏎
Using RREF directly:
```
[ 1  2 -1 |  8]
[-3 -1  2 |-11]
[-2  1  2 | -3]
```
R₂ → R₂ + 3R₁: [0, 5, -1 | 13]
R₃ → R₃ + 2R₁: [0, 5, 0 | 13]
R₃ → R₃ - R₂: [0, 0, 1 | 0]
z = 0
From R₂: 5y - 0 = 13, y = 13/5
From R₁: x + 2(13/5) - 0 = 8, x = 8 - 26/5 = 14/5
⏎
**Solution:** x = 14/5, y = 13/5, z = 0

# Parents

* Matrix equations