1. Using Matrices to Solve a 3-Variable System

2. (A Must be a square matrix)
Inverse Matrix
The product of a square matrix A and its inverse matrix A-1, on the left or the right, is the identity matrix I.
AA-1= A-1A =I
(A Must be a square matrix)
How do we find the Inverse Matrix:

3. Converting a Systems of Equations to a Matrix Equation
Make sure the equations are in alphabetical order
Identify all of the coefficients to the variables
Coefficient Matrix
Variable Matrix
Constant Matrix

4. Solving a Systems of Equations with Matrices
Solve:
Identify all of the coefficients to the variables
Make sure the equations are in alphabetical order and that every variable is in each equation
Coefficient Matrix “A”
Variable Matrix “X”
Constant Matrix “B”

5. Solving a Systems of Equations with Matrices
Continued… A X B
Which Order is Correct?
Multiply by the inverse of A to isolate the variable matrix
3x3.3x1
A-1 A X
A-1 B
3x1.3x3 OR
A-1 A X B
A-1

6. Solving a Systems of Equations with Matrices
Continued… A X B
Step 1: Store Matrix A and B in your calculator
Multiply by the inverse of A to isolate the variable matrix
A-1 A X
A-1 B
Step 2: Enter this in your calculator to solve the system
THUS:
You do not need to calculate the inverse matrix!
If…
Then…