"FILE: ECHELON"

"Requires the file VECTOR.MTH"

T_1(a,n,j,r):=ELEMENT(a,n,j) AND n<r

T_2(a,i,j,r):=SUM(ELEMENT(a,k,j)^2,k,i,r)

T_3(i,j,c,r):=j>c OR i>r

V_(a,i,j,r,c):=

U_(a,i,j,r,c):=IF(T_3(i,j,c,r),a,V_(a,i,j,r,c))

"####################"

"USER FUNCTIONS"

ECHELON(a):=U_(a,1,1,DIMENSION(a),DIMENSION(a`))

"************************"

"If this file beeped at you when you loaded it"

"reload it in two steps as follows"

"Transfer Load Utility VECTOR"

"Transfer Merge ECHELON"

"*********************"

"INSTRUCTIONS"

"ECHELON(A) returns an echelon form of the matrix, A"

"###################"

"EXAMPLE"

a:=[[3,5,4,6,7],[8,9,2,3,4],[1,2,3,5,3]]

"Simplify the following to see an echelon form of A"

ECHELON(a)

"IF THIS FILE BEEPED AT YOU, SEE THE NOTE ABOVE."