x, y = var('x, y')
h(x, y) = [x-y,x+y]
T = linear_transformation(QQ^2, QQ^2, h)
x1=vector([1, 1])
x2=vector([-1, 0])
y1=vector([1, 1])
y2=vector([-1, 0])
B=column_matrix([y1, y2, T(x1), T(x2)])
print B
print
C=B.echelon_form()
print C
print
A=C.submatrix(0, 2, 2, 2)
print A
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[ 1 -1 0 -1]
[ 1 0 2 -1]
[ 1 0 2 -1]
[ 0 1 2 0]
[ 2 -1]
[ 2 0]
[ 1 -1 0 -1]
[ 1 0 2 -1]
[ 1 0 2 -1]
[ 0 1 2 0]
[ 2 -1]
[ 2 0]
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