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INTERACTIVE MATRIX ROW OPERATIONS FOR TI CALCULATORS

This program does individual row operations on matrices. It can be used exactly as entered for either the TI-82 or TI-83.

This program and its companion program for the Casio Cfx-9850 Plus  were written as aids in teaching students the method of doing Gauss and Gauss-Jordan elimination without the confusion of two different calculators and without getting students bogged down in arithmetic. The student selects the type of row operation from a menu and then tells the calculator what multiplier and/or what rows are involved. The calculator displays the matrix with the completed operations.  The matrix must be entered into position A, but the working matrix is B.

What's new in V1.1?  I have included a menu item, #5, that allows multiplying two rows by a constant and then adding the rows.  This is convenient for avoiding fractions.  In V1.0, this could be done by using the multiply, *row(, and the *row+ functions in sequence, but most students seemed not to recognize that.   I had to eliminate QUIT because Menu only supports seven items.  No big deal; you can always quit the program by pressing OFF.  I have also changed the working matrix from A to B, but the data is still entered into matrix A.  Finally, as a housekeeping routine, I have entered the coding so that the labels are  in numerical order. 

NOTE: Every single move is not entered in the code entry instructions, e.g., when you are in 2nd MATRIX #9; and STO or ALPHA is the next step, naturally you must 2nd QUIT from the matrix menu. In the entry instructions, semicolons are used as separators and commas are as entered in the program. If there's any confusion, just enter all of the commas in the coding. I'm offering this program for free in exchange for any suggestions you may have to make the coding more efficient or the instructions clearer.

DISCLAIMER:  This program is free, and, therefore, I make no claims about it's efficacy, efficiency, or proper operation.  If you find a problem with this program, or can suggest an improvement, please e-mail me at knosummath@aol.com  .

Use of this Program:  You may use this  program  freely for your own personal use and for the use of other students, but use for publication or any means of profit requires my permission.

Memory Usage:  This version of the program uses 417 bytes of memory. I estimate it will take an inexperienced programmer about 20 minutes to enter by hand.

HELP: At the end of this coding is a matrix with row operations for you to check to see if everything is working okay.

CODING ENTRY

MAIN MENU

KEYSTROKES

:MATRWOP2

2nd ALPHA

Enter Text

:Disp "V1.1 fKizer"

PRGM
2ND ALPHA

I/O; 3
Text Entry

:[A] →[B]

2ND MATRIX
2ND MATRIX

1;STO
2

:Lbl 0

PRGM

CTL; 9; 0

:Pause [B]

PRGM
2ND MATRIX

CTL; 8
2

:Menu ("MTXOP", "SWP ROWS",1, " MULTPLY",2,"ADD  ROWS",3, "N*RW A+RWB",4,"N * RW A +M *RW B",5, "STRT OVR",6,"DEC TO FRAC",7)

PRGM
2ND ALPHA

CRL; C
For text entry.

:Lbl 1

PRGM

CTL 9; 0

:Input ("1ST ROW NUM " , J)

PRGM
2ND ALPHA

I/O; 1
For Text Entry

:Input ("2ND ROW NUM " ,K)

PRGM
2ND ALPHA

I/O; 1
For Text Entry

:rowSwap([B],J,K)→[B]

2ND MATRIX

 
 

2ND MATRIX

MATH; C

NAMES; 2;

ALPHA; J, K,) STO;
2

:Goto 0

PRGM

CTL; 0;0

:Lbl 2

PRGM

CTL; 9; 2

:Input ("MULTIPLIER ",N)

PRGM
2ND ALPHA

I/O;9
For Text Entry

:Input ( ROW NUM ",J)

PRGM
2ND ALPHA

I/O;9
For Text Entry

:*row(N, [B], J)→[B]

2ND MATRIX

2ND MATRIX

2ND MATRIX

MATH; E; ALPHA; N

2, ;ALPHA; J;); STO
2

:Goto 0

PRGM

CTL, 0, 0

:Lbl 3

PRGM

CTL, 9, 3

:Input ("1ST ROW NUM ",J)

PRGM
2ND ALPHA

I/O,9
For Text Entry

:Input ( "2ND ROW NUM ",K)

PRGM<
2ND ALPHA

I/O;9
For Text Entry

:row+([B],J,K)→[B]

2ND MATRIX

 

 

2ND MATRIX

MATH;D; NAMES; 2; ALPHA; J,K;);

STO;

2

:Goto 0

PRGM

CTL; 0; 0

:Lbl 4

   

 :Input ("MULTIPLIER ",N)

   

:Input ("1ST ROW NUM " , J)

   
:Input ("2ND ROW NUM " ,K)    

:*row+(N,[B],J,K)→[B]

   

:Goto 0

   

:Lbl 5

PRGM

CTL; 9; 4

 :Input "MULTIPLIER ",N

PRGM
2ND ALPHA

I/O;9
For Text Entry

:Input  "1ST ROW NUM" , J

PRGM
2ND ALPHA

I/O;9
For Text Entry

:Input  "MULTIPLIER ",M    

:Input  "2ND ROW NUM " ,K

PRGM
2ND ALPHA

I/O;9
For Text Entry

*row(M,[B],K)→[B] 2nd MATRIX

2nd MATRIX

2nd MATRIX

MATH; E; ALPHA M;
2; ALPHA; K; );STO

 

 

:*row+(N,[B],J,K)→[B]

2ND MATRIX

2ND MATRIX

2ND MATRIX

MATH; F
ALPHA; N,
2; ALPHA; J,K;); STO

2

:Goto 0

PRGM

CTL; 0; 0

:Lbl 6

PRGM

CTL; 9;5

:[A] →[B]

2ND MATRIX
2ND MATRIX

1; STO
2

:Goto 0

PRGM

CTL; 0

:Lbl 7

PRGM

CTL; 9; 7

:ClrHome

PRGM

I/O;8

:Disp [B]►Frac

PRGM

MATH

I/O;3

1

:Stop

PRGM

CTL;F

NOTE: We're not going to try to develop any clever strategy on this matrix. To minimize error propagation, we're are going to try to avoid fractions as long as possible. The format for my "shorthand" instructions will be this order; menu item number, first multiplier, first row, second multiplier, second row. If you get mixed up, start over by using menu item 5. That'll restore the original matrix in [A]. If you re-execute the program, your partially solved matrix will be transferred to [B] and you'll lose the original matrix. Alternatively, from the beginning, you could enter the matrix in [C]; then transfer it to [A] using these commands from the home screen: 2nd, MATRIX, 3, STO, 1. Then if you get mixed up you can start over just by transferring from [C] to [A] again.
(Note that Menu item 4 has been changed from the normal *row+ in order to implement the ability to multiply both rows by a constant.  This multiplying both rows by a constant is very useful to avoid fractions.  If you don't want to multiply one of the rows by a constant, just make the multiplier for that row 1.)

Here's an example problem:

Enter this matrix in [A]:

[ 2 1 -2 |1]
[-1 1 -3 |0]
[ 4 3  0  | 4]

(Read the instructions down the left side; then down the right.)

Go to your program and execute it.

Menu 2; 3R1;

Press ENTER and the matrix will be displayed.

Menu 4; -R2 +R1; Menu 2; 7R2; Menu 2;3R3

Press ENTER to display the menu.

Menu 4; -1R2+1R3; Menu 2; 20R1

We want to swap rows 1 and 2.

Menu 3; R3 + R1

Press 1 (SWP ROWS)

Menu 4: 56/20R3 + 1R2

Press 1, ENTER

Menu 2; -1/60R1; Menu 2; 1/21R2;Menu 2; 1/20R3

Press 2, ENTER

ENTER 7; ENTER

Now, I'll go to shorthand.

You should have x= 1/4, y = 1; z = 1/4

Menu 4; 2R1 + 1R2

 

Menu 4, 4R1 + 1R3

 

Revised:  10/2/04