x,y = var('x, y')
h(x,y) = [x+y, x-3*y, -2*x+y]
T = linear_transformation(QQ^2, QQ^3, h)
x1 = vector([1,1])
x2 = vector([2,1])
y1 = vector([1,0,-1])
y2 = vector([-1,2,1])
y3 = vector([0,1,1])
B = column_matrix([y1, y2, y3, T(x1), T(x2)])
B = column_matrix([y1, y2, y3, T(x1), T(x2)])
print B
print
C = B.echelon_form()
print C
print
A = C.submatrix(0,3,3,2)
print A
|
|
[ 1 -1 0 2 3]
[ 0 2 1 -2 -1]
[-1 1 1 -1 -3]
[ 1 0 0 1/2 5/2]
[ 0 1 0 -3/2 -1/2]
[ 0 0 1 1 0]
[ 1/2 5/2]
[-3/2 -1/2]
[ 1 0]
[ 1 -1 0 2 3]
[ 0 2 1 -2 -1]
[-1 1 1 -1 -3]
[ 1 0 0 1/2 5/2]
[ 0 1 0 -3/2 -1/2]
[ 0 0 1 1 0]
[ 1/2 5/2]
[-3/2 -1/2]
[ 1 0]
|