## Solving Systems of Linear Equations Using Matrices

Example

Solve

x + y + z = 6

2y + 5z = −4

2x + 5y − z = 27

## Change into matrix form *AX = B*

where

*A*is the 3×3 matrix of*x, y, z*coefficients*X*is*x, y, z**B*is 27, 6, −4

## Then find the value of *x, y, z*

*X = A*^{-1}*B*

*A*^{-1 }=

So

*X = A ^{-1}B = *

## Solution

The solution is

*x* = 5

*y* = 3

*z* = -2