Application:  Notice that this program is not listed for the TI-83 Plus. It will work for the TI-83 series, but since rref and ref are built in on the TI-83, there is not much need for it.  I would mention that this offers a couple things that are not in the TI-83 Plus. For example, Upper Triangle display, and better treatment of non-orthodox matrices

Memory usage:  This program uses 972 bytes of memory.  I estimate that an inexperienced programmer can enter it in about 35 to 40 minutes.

Running the Program: First store your matrix in position [A]. After starting the program, the matrix is displaye, for checking if desired, and the program is paused.  A menu is then presented that allows selection of either rref,  ref, or upper triangle.   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 Plus with some additions.  There should not be any divide-by-zero errors.  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 V1.1, 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.  Version 2.0, date 2/23/05 has the changes mentioned above.  There are no keystrokes listed for this program.  After 4/28/05, keystrokes will no longer be included in programs.

Program: TI82GsJr
:Disp "F KIZER"
:Disp "V 2.0 2235"
:Lbl 0
:0→J
:0→K
:dim [A]→L₁
:L₁(1)→R
:L₁(2)→C
:[A]→[B]
:Pause [B]
:For(K,1,C-2)
:0→P
:For(J,K,R)
:If [B](K,K)≠1 and [B](J,K)=1 and P=0
:Then
:rowSwap([B],J,K)→[B]
:P+1→P
:End
:If [B](K,K)=0 and [B](J,K)≠0
:Then
:rowSwap([B](J,K)→[B]
:End:End
:For(J,K+1,R)
:-[B](K,K)→M
:[B](J,K)→N
:If M≠0 and N≠0
:Then
:*row(M,[B],J)→[B]
:*row+(N,[B],K,J)→[B]
:End:End:End
:ClrHome
:Output(2,1,"1:RREF")
:Output(3,1,"2:REF")
:Output(4,1,"3:UP TRIANG")
:Input "ENTER NO."  S
:If S=3 and C≤5
:If S=3
:Goto 7
:If C>R+1
:Goto 6
:For(K,1,C-1)
:[B](K,K)→Q
:If Q≠0 and Q≠1
:Then
:*row(1/Q,[B],K)→[B]
:End:End
:If S=2 and C≤R
:Goto 5
:If S=2:Goto 7
:If  C≤R
:Goto 4
:R-1→W
:For(K,C-1,2,-1)
:For(J,W,1,-1)
:If [B](K,K)≠0 and [B](J,K)≠0
:Then
:-[B](J,K)/[B](K,K)→T
:*row+(T,[B],K,J)→[B]
:End:End
:W-1→W
:End
:If C=R+1
:Goto 7
:Lbl 4
:If C≤R
:Then
:C-2→W
:For(K,C-1,2,-1)
:For(J,W,1,-1)
:If [B](K,K)≠0 and [B](J,K)≠0
:Then
:-[B](J,K)/[B](K,K)→Y
:*row+(Y,[B],K,J)→[B]
:End:End
:W-1→W
:End

Lbl 5
:If C≤R
:Then
:C-1→K
:For(J,C,)
:If  [B](K,K)≠0 and [B](J,K)≠0
:Then
:-[B](K,K)→D
:[B](J,K)→E
:*row(D,[B],J)→[B]
:*row+(E,[B],J,K)→[B]
:End:End:End
:Lbl 6
:If C>R+1
:Then
:For(K,1,R)
:B(K,K)→Q
:If Q≠0 and Q≠1
:Then
:*row(1/Q,[B],K)→[B]
:End:End:End
:If S=1 and C>R+1
:Then
:R-1→Z
:For(K,R,1,-1)
:For(J,Z,1,-1)
:If [B](K,K)≠0 and [B](J,K)≠0
:Then
:-[B](J,K)/[B](K,K)→G
:*row+(G,[B],K,J)→[B]
:End:Rnd
:Z-1→Z
:End:End
:Lbl 7
:For(K,1,C)
:For(J,1,R)
:[B](J,K)→H
:If √(H²)<1E-7
:Then
:0→[B](J,K)
:End:End:End
:ClrHome
:Pause [B]►Frac