x,y = var('x, y')
h(x,y) = [x-y, x+y]
T = linear_transformation(QQ^2, QQ^2, h)
x1 = vector([1,2])
x2 = vector([-1,1])
y1 = vector([1,2])
y2 = vector([-1,1])
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 -1 -2]
[ 2 1 3 0]
[ 1 0 2/3 -2/3]
[ 0 1 5/3 4/3]
[ 2/3 -2/3]
[ 5/3 4/3]
[ 1 -1 -1 -2]
[ 2 1 3 0]
[ 1 0 2/3 -2/3]
[ 0 1 5/3 4/3]
[ 2/3 -2/3]
[ 5/3 4/3]
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