Gaussian Elimination on a TI-83 Plus

Consider the following system of linear equations:

4x1 + 3x2 =  7
 x1 +  x2 = -1

Enter the System as a Matrix

1. To enter a matrix, begin by entering this keystroke combination: 2nd Matrix

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

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

2 Enter 3 Enter

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

4 Enter 3 Enter 7 Enter 1 Enter1 Enter -1 Enter

5. When you are done, press 2nd Quit.

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

1. Press 2nd Matrix

2. Select the Math option.

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

TI-83 Display

4. Press 2nd Matrix and with matrix A selected Enter and close the parentheses. The screen display will look like this:

TI Display

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

Reduced Row Echelon Form 

In this form, it should be apparent that x1 = 10 and x2 = -11.