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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