x, y, z = var('x, y, z')
h(x, y, z) = [3*x-2*z,6*y-2*z]
T = linear_transformation(QQ^3, QQ^2, h)
x1=vector([0,0,1])
x2=vector([0,1,1])
x3=vector([-1,0,-2])
y1=vector([2,0])
y2=vector([0,1])
B=column_matrix([y1, y2, T(x1), T(x2), T(x3)])
print B
print
C=B.echelon_form()
print C
print
A=C.submatrix(0, 2, 2, 3)
print A
|
|
[ 2 0 -2 -2 1]
[ 0 1 -2 4 4]
[ 1 0 -1 -1 1/2]
[ 0 1 -2 4 4]
[ -1 -1 1/2]
[ -2 4 4]
[ 2 0 -2 -2 1]
[ 0 1 -2 4 4]
[ 1 0 -1 -1 1/2]
[ 0 1 -2 4 4]
[ -1 -1 1/2]
[ -2 4 4]
|