Solving Linear Systems on the TI-85

Gary A. Harris

Department of Mathematics

Texas Tech University

Lubbock, Texas

g.harris@ttu.edu

Propose:	To introduce the students to the SIMULT package on the TI-85.

Target:	The students gain skill using the SIMULT package of the TI-85 and understand to two different phenomenon that can occur when the system is singular.

A. Solve each of the following systems "by hand," clearly indicating all the steps.

1.	x + y + z = 3

-x + 2y - z = 0

3x - y + 2z = 2

2.	x +5y - z = 2

4x - y + 3z = 3

8x - 2y + 6z = 7

3.	3x + y + z = 0

-5x + 5y + z = 0

x + 2y + z = 0

The TI-85, henceforth referred to as "IT", has a built-in package for solving systems of n linear equations in n unknowns. We will use IT to solve each of the above problems 1-3. To access this package choose 2nd SIMULT from the keyboard. IT asks for the Number=, meaning the number of equations and (equal) number of unknowns (the n above).

For our purpose choose Number= 3. (Press 3 then ENTER from the keyboard.) IT now asks for the coefficients of the 1st equation.

a1,1 is the first coefficient in the first equation,

a1,2 is the second coefficient in the first equation,

a1,3 is the third coefficient in the first equation, and

b1 is the constant in the first equation.

To enter problem #1 above into IT we enter

a1,1= 1	(Press 1 and arrow down from the keyboard.)

a1,2= 1	(Press 1 and arrow down from the keyboard.)

a1,3= 1	(Press 1 and arrow down from the keyboard.)

b1= 3	(Press 3 and arrow down from the keyboard.)

Now IT asks for the coefficients of the second equation. Enter them in similar fashion.

a2,1= -1	(Remember to use (-) 1 to enter the negative of 1.)

a2,2= 2

a2,3= -1

b2= 0

Finally IT asks for the coefficients of the third equation. Enter them, again in similar fashion.

a3,1= 3

a3,2= -1

a3,3= 2

b3= 2

(You can up arrow back through the entries to double check to see if they are correct, if you wish.)

Now for the moment of truth: choose SOLVE from the bar menu (F5) and record the result. Does it check with you "hand calculation?" I bet IT was quicker, once you got the problem into the machine that is.

To enter a new 3 by 3 system into IT choose COEFS from the bar menu. This let's you change the coefficients to the ones in the new system by repeating the process described above.

What is IT's result for problem 2?

What is IT's result for problem 3?

Notice, unfortunately IT does not distinguish between the very different phenomenon that occurs and problem 2 and 3. If your life depended on finding values for x, y, and z that satisfied a given 3 by 3 system of linear equations, which system would you prefer to be dealing with, #1, #2, or #3? Why?

With which of these systems would you be doomed? Why?

If you are trying to solve a system and IT replies "ERROR 03 SINGULAR MAT", what do you do next? (Remember, your life, not to mention your grade, depends on it.)