1. Matrix Equations
Step 1: Write the system as a matrix equation. A three-equation system is shown below. First matrix are the coefficients of all the x, y, z variables. Second matrix are your variables. Third matrix are the constants, what the equations equal. Make sure the matrix is in alphabetical order!!!

2. Matrix Equations
Step 2: Go to your calculator – 2nd x^-1 (matrix key). Go over to EDIT. Enter the size of the matrix with number of rows first then number of columns second. Enter in all the coefficients from matrix A.
Step 3: Go back to 2nd x^-1 (matrix key). Go over to EDIT. Enter the size of the matrix and enter the constants (what the equations are equal to).

3. Matrix Equations
Step 4:Go back to your main screen. Now choose matrix A, click x^-1 key, choose matrix B. Should look like A^-1B. Press enter. This will give you your answers!
Note: The multiplication order on the right side is very important. We cannot multiply a 3 x 1 times a 3 x 3 matrix!

4. Matrix Equations
Example: Solve the system 3x - 2y = x + 2y = -5

5. Matrix Equations
Example, continued: (Answer!)

6. Matrix Equations
Example #2: Solve the 3 x 3 system 3x - 2y + z = 9 x + 2y - 2z = -5 x + y - 4z = -2
Using a graphing calculator,
Matrix A is the first one, Matrix B is the last one

7. Matrix Equations
Example #2, continued