Solving Systems of Equations with Three Variables Using Matrices

In a previous section you learned how to solve systems of equations in two variables using matrices. The process is the same when we move up the three variables.

The following still holds true:

AX = B

A^-1(AX) = A^-1B

(A^-1A)X = A^-1B

IX = A^-1B

Therefore, X = A^-1B.

To solve a system of equations:

1. first set up your matrix equation
2. find the inverse of matrix A
3. multiply the inverse by matrix B

This same process can be used to solve for any number of variables as long as you have the same number of equations.