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CASIO INTERACTIVE MATRIX ROW OPERATIONS

This is a program for the Casio Cfx-9850 Plus that does individual row operations on matrices

This program and its companion program for the TI-82/83 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 (matrix A is used) with the completed operations.

Although the syntax of this program is different from the program for the TI-83, what the user sees within the program will be very similar with the two calculators. So the instructor/tutor can use this when teaching a group that has both types of calculators.

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 have also changed the working matrix from A to B, but the data is still entered into matrix A. 

SNYTAX NOTE: The symbol => is not equal to or greater than, but is the symbol obtained by [SHIFT], [PRGM],[F3],[F3]. The symbol ∆ is not a triangle, but the symbol obtained by [SHIFT], [PRGM],[F3].

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  .

Memory Usage:  This program uses 433 bytes of memory.  I estimate it will take an inexperienced programmer about 20 minutes to enter this program by hand.

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.

Enter the following for the program:

CODE ENTRY

FIRST LEVEL

NEXT LEVEL(S)

     

CMTRWOP2

SHIFT, ALPHA

Enter Text (Cancel APLHA for numbers.)

"V1.1 FKizer"

SHIFT; ALPHA

Enter Text

Mat A →Mat B

OPTN

F2;F1; A;® F2;F1;B

Lbl 0

SHIFT; PRGM

F3;F1; 0

Mat B∆

OPTN
SHIFT; PRGM

F2; F1; A;
F5

" 1 SWP ROWS"

SHIFT; ALPHA

Enter Test & Numbers

"2 MULTIPLY"

SHIFT; ALPHA

Enter Test & Numbers

"3 ADD ROWS"

SHIFT; ALPHA

Enter Test & Numbers

"4 N * RW A + RW B"

SHIFT; ALPHA

Enter text & Characters

"5  N*RW A + M * RW B"    

"6 STRT OVER"

SHIFT; ALPHA

Enter Text & Numbers

"7 QUIT"

SHIFT; ALPHA

Enter Text & Numbers

?→V

SHIFT; PRGM
ALPHA

F4; ®
V

V = 1=> Goto 1

ALPHA
SHIFT, PRGM

V
F6;F3;F1;1;EXIT;F6;F3;F2;1

V = 2 =>Goto 2

ALPHA
SHIFT, PRGM

V
F6;F3;F1;2;EXIT;F6;F3;F2;2

V = 3 => Goto 3

ALPHA
SHIFT, PRGM

V
F6;F3;F1;3;EXIT;F6;F3;F2;3

V = 4 =>Goto 4

ALPHA
SHIFT, PRGM

V
F6;F3;F1;4;EXIT;F6;F3;F2;4

V = 5=> Goto 5

ALPHA

SHIFT, PRGM

V

F6;F3;F1;5;EXIT;F6;F3;F2;5

V = 6 =>Goto 6

ALPHA
SHIFT, PRGM

V
F6;F3;F1;6;EXIT;F6;F3;F2;6

V=7=>Toto 7    

Lbl 1

SHIFT; PRGM

F3;F1; 1

"ENTR 1ST ROW NO"?→J

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® J

"ENTR 2ND ROW NO "?→K

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® K

Swap B, J, K

SHIFT; PRGM;
EXIT; ALPHA

F2; F1
Enter commas & Letters

Goto 0

SHIFT, PRGM

F3;F2;0

Lbl 2

SHIFT; PRGM

F3;F1; 2

"ENTR MULTPLER"?→N

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® N

"ENTR ROW NO"? →J

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® J

*row N, B, J

SHIFT; PRGM;EXIT
ALPHA

F4;F2; F2
Enter commas & Letters

Goto 0

SHIFT, PRGM

F3;F2;0

Lbl 3

SHIFT; PRGM

F3;F1; 3

"ENTR 1ST ROW NO"?→J

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® J

"ENTR 2ND ROW NO "?→K

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® K

row+ B,J,K

SHIFT; PRGM;EXIT
ALPHA

F4;F2; F4
Enter commas & Letters

Goto 0

SHIFT, PRGM

F3;F2;0

Lbl 4

SHIFT; PRGM

F3;F1; 4

"ENTR MULTPLER"?→N

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® N

"ENTR 1ST ROW NO"?→J

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® J

"ENTR 2ND ROW NO "?→K

SHIFT; ALPHA
SHIFT; PRGM

Enter Text & Numbers
F4;® K

*row+ N,B,J,K

SHIFT; PRGM;EXIT
ALPHA

F4;F2; F3
Enter commas & Letters

Goto 0

SHIFT, PRGM

F3;F2;0

Lbl 5    
"ENTR 1ST  MULTPLER"?→N    
"ENTR 1ST ROW NO"?→J    
"ENTR 2ND  MULTPLER"?→M    
"ENTR 2ND  ROW NO"?→K    
*row M, B, K    
*row+ N,B,J,K    
Goto 0    

Lbl 6

SHIFT; PRGM

F3;F1; 5

Mat A→Mat B

OPTN

F2;F1; B;® F2;F1;A

Goto 0

SHIFT, PRGM

F3;F2;0

Lbl 7

SHIFT; PRGM

F3;F1; 6

Stop

SHIFT; PRGM

F2;F4

Now, let's do a matrix to make sure everything is okay.

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, multiplier, first row, second row. If you get mixed up, start over by using menu item 6. That'll restore the original matrix in [B].  Alternatively, from the beginning, you could enter the matrix in [C]; then transfer it to [A] using these commands from the home screen: SHIFT; PRGM; F2;F1;ALPHA, C,® F1;A. Then if you get mixed up you can start over just by transferring from [C] to [A] again.

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 EXE and the matrix will be displayed.

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

Press EXE to display the menu.

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

We want to swap rows 1 and 2.

Menu 3; R3 + R1

Press 1 (SWP ROWS)

Menu 4: 56/20R3 + R2

Press 1;EXE;

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

Press 2; EXE

You should have x= 0.25, y = 1; z = 0.25

Now, I'll go to shorthand.

*See the note below to covert to the answer to fractions.

Menu 4; 2R1 + R2

 

Menu 4, 4R1 + R3

 

If you want to convert the answers to fractions, do the following:
1)  Quit the program and go to Menu and click the MAT icon.
2)  Edit Matrix A.  Place the cursor on the entry you want to convert; then press F<->D.  The entry will appear
     near the bottom right of the screen.


Last Revised: 10/27/09