Table of Contents

Solving Linear Systems of Equations - Calculator Methods

• Consider the following augmented matrix ...

5100

7010

3001

• 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!

Table of Contents Slide 2

Solving Linear Systems of Equations - Calculator Methods

5100

7010

3001• 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.

Table of Contents Slide 3

Solving Linear Systems of Equations - Calculator Methods

• Example 1: Solve the system of equations using RREF on a calculator.

0z4yx3

5z2y2x

3z2yx5

• 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.

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 ...

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 ...

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 ...

BAX represents a linear system, then the solution is ...

BAX 1

Table of Contents Slide 4

Solving Linear Systems of Equations - Calculator Methods

0z4yx3

5z2y2x

3z2yx5

• 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 ...

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 ...

Table of Contents

Solving Linear Systems of Equations - Calculator Methods