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^-1B

A^-1 =

So

X = A^-1B =

Solution

The solution is

x = 5

y = 3

z = -2

Learn More

General Form of Equation of a Line

Solving SAS Triangles

Conjugate

Rationalize the Denominator

Algebra Index