1. Table of Contents Solving Linear Systems of Equations - Calculator Methods Consider the following augmented matrix... The rows can be written as... Row 1: x + 0y + 0z = 3  x = 3 Row 2: 0x + y + 0z = -7  y = -7 Row 3: 0x + 0y + z = 5  z = 5 The solutions of the system are simply found in the last column!

2. Table of Contents Slide 2 Solving Linear Systems of Equations - Calculator Methods The augmented matrix is said to be in Reduced-Row- Echelon form, or RREF. When solving a system of linear equations that has a unique solution, the RREF function on a calculator can be used to very quickly find the solution.

3. Table of Contents Slide 3 Solving Linear Systems of Equations - Calculator Methods Example 1: Solve the system of equations using RREF on a calculator. Enter the augmented matrix into the calculator. See the presentation on “Matrices - Calculator Operations” is you need help with this. Note that only columns 2 - 4 are showing.

4. Table of Contents Slide 4 Solving Linear Systems of Equations - Calculator Methods Press 2nd|QUIT, then MATRIX and right arrow to MATH... Go down in the list to rref( which is item B, and press ENTER... This places rref( on the home screen. Now press MATRIX and ENTER to select matrix A...

5. Table of Contents Slide 4 Solving Linear Systems of Equations - Calculator Methods Press ENTER... The solutions to the system are found in the last column. To show the answers as fractions, press MATH|ENTER|ENTER...

6. Table of Contents Slide 4 Solving Linear Systems of Equations - Calculator Methods Another method that works nicely on the calculator to solve linear systems is in using inverse matrices. Recall that if the matrix equation... represents a linear system, then the solution is...

7. Table of Contents Slide 4 Solving Linear Systems of Equations - Calculator Methods Example 2: Solve the system of equations using an inverse matrix on a calculator. Write matrix A, the coefficients, into the calculator... Write matrix B, the constants, into the calculator...

8. Table of Contents Slide 4 Solving Linear Systems of Equations - Calculator Methods Press 2nd Quit and then MATRIX|ENTER to place matrix A on the home screen... Press the x -1 key, then MATRIX|2 to place matrix B on the home screen... Press ENTER... and the solutions are listed. To write the solutions as fractions, press MATH|ENTER|ENTER...

9. Table of Contents Solving Linear Systems of Equations - Calculator Methods