x, y = var('x, y')
h(x, y) = [-5*x+6*y,-3*x+4*y]
T = linear_transformation(QQ^2, QQ^2, h)
x1=vector([1,1])
x2=vector([0,1])
y1=vector([-1,-1])
y2=vector([2,1])
B=column_matrix([x1, x2, T(x1), T(x2)])
print B
print
C=B.echelon_form()
print C
print
T=C.submatrix(0, 2, 2, 2)
print T
print
D=column_matrix([x1, x2, y1, y2])
print D
print
E=D.echelon_form()
print E
print
F=E.submatrix(0, 2, 2, 2)
print F
G=F.inverse()
print
print G*T*F
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[1 0 1 6]
[1 1 1 4]
[ 1 0 1 6]
[ 0 1 0 -2]
[ 1 6]
[ 0 -2]
[ 1 0 -1 2]
[ 1 1 -1 1]
[ 1 0 -1 2]
[ 0 1 0 -1]
[-1 2]
[ 0 -1]
[ 1 0]
[ 0 -2]
[1 0 1 6]
[1 1 1 4]
[ 1 0 1 6]
[ 0 1 0 -2]
[ 1 6]
[ 0 -2]
[ 1 0 -1 2]
[ 1 1 -1 1]
[ 1 0 -1 2]
[ 0 1 0 -1]
[-1 2]
[ 0 -1]
[ 1 0]
[ 0 -2]
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