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 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 above).
For our purpose choose Number= 3. ( Press 3 then ENTER from the
keyboard.) IT now asks for the coefficients of the 1st equation.
is the first coefficient in the first
equation,
is the second coefficient in the first
equation,
is the third coefficient in the first
equation, and
is the constant in the first equation.
To enter problem #1 above into IT we enter
(Press 1 and arrow
down from the keyboard.)
(Press 1 and arrow down from the
keyboard.)
(Press 1 and arrow down from the
keyboard.)
(Press 3 and arrow down from the
keyboard.)
Now IT asks for the coefficients of the second equation. Enter
them in similar fashion.
(Remember to use (-) 1 to enter the
negative of
1.)
Finally IT asks for the coefficients of the third equation.
Enter them, again in similar fashion.
(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.)
