x,y,z=var('x,y,z')
a(x,y,z)=[x+y+z,y+z,-x+2*y-z]
T=linear_transformation(QQ^3,QQ^3,a)
x1=vector([1,1,1])
x2=vector([-1,0,1])
x3=vector([2,1,-1])
B=column_matrix([x1,x2,x3,T(x1),T(x2),T(x3)])
C=B.echelon_form()
D=C.submatrix(0,3,3,3)
print B
print
print C
print
print D
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[ 1 -1 2 3 0 2]
[ 1 0 1 2 1 0]
[ 1 1 -1 0 0 1]
[ 1 0 0 1 -1 3]
[ 0 1 0 0 3 -5]
[ 0 0 1 1 2 -3]
[ 1 -1 3]
[ 0 3 -5]
[ 1 2 -3]
[ 1 -1 2 3 0 2]
[ 1 0 1 2 1 0]
[ 1 1 -1 0 0 1]
[ 1 0 0 1 -1 3]
[ 0 1 0 0 3 -5]
[ 0 0 1 1 2 -3]
[ 1 -1 3]
[ 0 3 -5]
[ 1 2 -3]
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