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TI-82 Gauss & Gauss Jordan Elimination (rref & ref)

Application:  Notice that this program is not listed for the TI-83 Plus. It will work for the TI-83, but since rref and ref are built in on the TI-83, there is no need for it.

Memory usage:  This program uses 547 bytes of memory.  I estimate that an inexperienced programmer can enter it in about 25 to 30 minutes.

Running the Program: First store your matrix in position [A]. After starting the program, a menu is presented that allows selection of either rref or ref.   As usual with matrices, I recommend that when you enter a new matrix, you enter each element, rather than just replacing those that are different.  The answer is displayed in fractions.  Engineering and science students and others who prefer decimals, just look at matrix [B].  The fractional answer is not stored in a matrix; only displayed on the home screen.

Comments: This program operates similar to the ref and rref functions on the TI-83 in that in some instances inconsistent or dependent equations will give a "divide by zero" error for the rref function. You can usually see what the problem is if you use ref. I've checked this version, 1.12, out on about 30 different matrices, but if you have any problems, please send an e-mail to me, the Webmaster.  I would also appreciate any suggestions you might have for improving the coding.   STCC students, please e-mail me at: fkizer@southwest.tn.edu

Revisions:  Version V1.0, date 8/23/03.  Version V1.1, date 12/13/04.  Version V1.2, 10/7/04.  There are some fairly significant changes from V1.1 to V1.2.  The working matrix has been changed from [A] to [B], and several lines have been added at the end to correct for the annoying characteristic the TI-82 has of displaying a number such as 1.2E-14 for 0.

 CODE ENTRY KEYSTROKES NOTES Disp "V1.2 FKIZER" PRGM; I/O; 3 2nd ALPHA (Enter Text) Lbl 0 PRGM; CTL; 9 0→J:0→K Initialize dim ([A])→ L1 Gets dimension of matrix [A]. L1(1)→ R L1(2)→ C If C ≠ R+1 Checks if augmented. Then Disp "INVALID MATRIX" Stop End [A]→[B] For use with STRT OVR and reduces error propagation. For (K,1, C-2) PRGM; 4; First For( loop. 0→N For (J,K,R) Sort to get 1 in a11 position. If [B](K,K)≠ 1 and [B](J,K)=1 Then rowSwap([B],J,K)→[B] Stores rowswap in matrix [A]. N+1→N Indicates if 1 is found. Else If no "1", look for non-zero. If [B](K,K)=0 and [B](J,K)≠ and N=0 Then rowSwap([B],J,K,)→[B] End: End: End: For(J,K+1,R) For( loop for reduction. If [B](K,K)≠ 0 Then -[B](J,K)/[B](K,K)→H Multiplier for row operation. If H≠0 Then *row+(H,[B],K,J)→[B] Do row operation. End:End:End:End Menu("SELECT","RREF",1,"REF",2,"STRT OVR",3) Lbl 1 Starts elimination after ref. R→L For(K, C-1,2,-1) Decrements loop counter. For(J,R-1,1,-1) If [B](K,K)≠0 Minimize div by zero errors. Then -[B](J,K)/[B](K,K)→P Multiplier for row operation. *row+(P,[B],K,J)→[B] End:End R-1→R Decrement R. End Lbl 2 Starts reducing major diagonal to 1s. For(K,1,C-1) If [B](K,K)≠0 Minimize div by zero errors. Then 1/[B](K,K)→T Divisor stored in variable T. *row(T,[B],K)→[B] End:End ClrHome Clear Screen L-->R For(J,1,R) For(K,1,C) If abs([B](J,K)≤1.0E-9 E is 2nd, EE Then 0→[B](J,K) End:End:End Pause  [B]►Frac Converts decimals to fractions Stop End of ref and rref. Lbl 3 Object of STRT OVR in menu. Goto 0

Revised: 10/7/04