Untitled

512 days ago by s2s2111

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 
       
[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]