1. Solving Systems in 3 Variables using Matrices
1.7 Notes

2. What is an augmented matrix?
This matrix uses the coefficients and the constant to write a matrix which will allow us to use the calculator to find the solution to a three variable system.
If we are missing any values in our system, we MUST add a ZERO for that value to make our matrix work.

3. Write an augmented matrix for each system:
EX 1: EX 2:
x + z = x – 2y – 4z = 3
x + y + 2z = x + 3y + 2z = -3
x + 2y + z = x + 5y + 3z = 3

4. Solve using an augmented matrix:
EX 1: EX 2:
x + z = x – 2y – 4z = 3
x + y + 2z = x + 3y + 2z = -3
x + 2y + z = x + 5y + 3z = 3

5. Now that we have an augmented matrix…
We use the RREF function in our calculator to solve the system.
RREF is found under the MATH tab in the MATRIX operations.
Let’s try some:

6. Solve the following 3 variable system:
1) 2x + 3y + 7z = 13
3x + 2y - 5z = -22
5x + 7y – 3z = -28

7. 1) 2x - 4y + 3z = 17
x + 2y – z = 0
4x – y - z = 6