## Gaussian Elimination on a TI-83 Plus

Consider the following system of linear equations:

4x_{1} + 3x_{2} = 7
x_{1} + x_{2} = -1

### Enter the System as a Matrix

1. To enter a matrix, begin by entering this keystroke combination:

2. Use the cursor keys to select the **Edit** option and then
select row 1 (matrix
A). Press
.

3. Enter the dimensions of the coefficient matrix (2 rows by 3 columns):

2
3

4. Enter the values of the coefficient matrix (row by row):

4
3
7
1
1
-1

5. When you are done, press
.

### Display the Reduced Row Echelon Form (rref) of the Matrix

1. Press

2. Select the **Math** option.

3. Select the **rref(** option and
press
. The screen
display will look like this:

4. Press
and with matrix A selected
and close the
parentheses. The screen display will look like this:

5. Press
a second time
and the reduced row echelon form of the augmented matrix will be displayed:

In
this form, it should be apparent that x_{1} = 10 and x_{2} = -11.