MATH122

Finding Reduced Row Echelon Form on the TI-83

Use reduced row echelon form on the TI-83 to solve the linear system.

x + 2y - z - 3w = 2

3x + y - 2z - w = 6

x + y + 3z - 2w = -3

-2x - 2y + 3z + w = -9

The process of Gaussian elimination will allow the system to be rewritten in triangular form so that finding the solutions is ‘easy.’ When only the coefficients and constant terms are put into an augmented matrix, the corresponding triangular form is called echelon form. Your calculator can also use the process to find either echelon form or reduced row echelon form of the augmented matrix for the linear system. You must still interpret the results and write the solutions. The augmented matrix for the given system is

Use the following steps to enter the matrix into the TI-83 and put it in reduced row echelon form.

MATRX

4

4

1. Highlite EDIT; see on screen 1: [A]

2: [B]

3: [C]

4: [D]

1

5: [E]

2. Edit (enter) matrix [A]

5

ENTER

ENTER

4

3. Matrix [A] has 4 rows and 5 columns

1

4. and so on Enters the matrix values in row 1; the line on screen such as

1,4 = -3 means that the row 1, column 4 entry is -3

5. Enter the numbers in rows 2, 3, and 4

2nd

MODE

6. Quit out of the matrix menu

MATRX

ALPHA

4

MATRX

7. Use matrix math process ‘B’, which is rref (

1

MATRX

8. The screen should now read rref([A]

ENTER

9. The reduced row echelon form of A appears. You may need to use the right arrow key to see all of it.

10. Interpret the result. In this case, the solution is x = 1, y = 3, z = -1, w = 2 or (1, 3, -1, 2)