TI - 83 (PROJECT 2)



TI - 82/83

SOLVING SYSTEMS OF LINEAR EQUATIONS

using the work of paul vaz

1. Use elementary row operations on your graphing calculator to find the reduced row-echelon form of the augmented matrix to solve the system:

[pic]

Solution:

The augmented matrix is given by:

[pic]

Enter the matrix under matrix name [A] and quit.

Now press the following keys in the order given below:

Note that the first column is in already in the reduced form. Next we need a 1 in second row, second column position. We can obtain this easily by switching row 2 and 4.

1. MATRIX ( ( ( 12 times) ENTER (to switch two rows)

2. MATRIX ENTER , 2 , 4 ) ENTER

3. STO MATRIX ( ENTER ENTER

Next we want to obtain 0s in the second column above and below the 1:

4. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

5. (-) 4 , MATRIX ( ENTER , 2 , 4 ) ENTER

6. STO MATRIX ( ENTER ENTER

7. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

8. 2 , MATRIX ( ENTER , 2 , 1 ) ENTER

9. STO MATRIX ( ENTER ENTER

Next we need a 1 in third row, third column position. And luckily we have it.

Next we want to obtain 0s in the third column above and below the 1:

10. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

11. -3 , MATRIX ( ENTER , 3 , 1 ) ENTER

12. STO MATRIX ( ENTER ENTER

Next we need a 1 in fourth row, fourth column position. We can obtain this by multiplying the fourth row by -1/2:

13. MATRIX ( ( (14 times) ENTER (to obtain *row( )

14. (-) 1 [pic] 2 , MATRIX ( ENTER , 4 ) ENTER

15. STO MATRIX ( ENTER ENTER

Next we want to obtain 0s in the fourth column above the 1:

16. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

17. 1 , MATRIX ( ENTER , 4 , 3 ) ENTER

18. STO MATRIX ( ENTER ENTER

19. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

20. -2 , MATRIX ( ENTER , 4 , 2 ) ENTER

21. STO MATRIX ( ENTER ENTER

22. MATRIX ( ( (15 times) ENTER ( to obtain *row+( )

23. -3 , MATRIX ( ENTER , 4 , 1 ) ENTER

The reduced row-echelon form of the matrix is

[pic]

Thus, the solution is:

[pic]

2. Use ‘rref’ on your graphing calculator to find the same answer as above in one step. Make sure you start with the original matrix A!!!

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