x, y, z = var('x, y, z')
h(x, y, z) = [2*x-z,z+3*y,x-2*y]
T = linear_transformation(QQ^3, QQ^3, h)
x1=vector([1, 2, -1])
x2=vector([-1, 0, 4])
x3=vector([3, -5, 2])
B=column_matrix([x1, x2, x3, T(x1), T(x2), T(x3)])
print B
print
C=B.echelon_form()
print C
print
A=C.submatrix(0, 3, 3, 3)
print A
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[ 1 -1 3 3 -6 4]
[ 2 0 -5 5 4 -13]
[ -1 4 2 -3 -1 13]
[ 1 0 0 115/43 -69/43 -37/43]
[ 0 1 0 -5/43 3/43 82/43]
[ 0 0 1 3/43 -62/43 97/43]
[115/43 -69/43 -37/43]
[ -5/43 3/43 82/43]
[ 3/43 -62/43 97/43]
[ 1 -1 3 3 -6 4]
[ 2 0 -5 5 4 -13]
[ -1 4 2 -3 -1 13]
[ 1 0 0 115/43 -69/43 -37/43]
[ 0 1 0 -5/43 3/43 82/43]
[ 0 0 1 3/43 -62/43 97/43]
[115/43 -69/43 -37/43]
[ -5/43 3/43 82/43]
[ 3/43 -62/43 97/43]
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