Thread: y=2x mapped onto itself under transformation T

, where k is constant
A transformation T:R^2 arrow R^2 is represented by the matrix A.
Find the value of k for which the line y=2x is mapped onto itself under T.


What I did:
=
implies =
Therefore k=5 and k=1 !!
What I should do:
x(1+k)=2x(k-4)
k=9
Where is my principle wrong? Please point it out, because i fear its something fundamental and i may have to suffer direly for it later.
edit:k=5, k=1

Hi,
your principle is wrong because by = you're saying that a point (x,2x) must map to itself. This condition is too strong and as you showed it has no solution for k. What you have to consider is (because (x,2x) can be mapped to arbitrary point (w,2w))
and after eliminating w from two simultaneous equations you get the right result (or you get necessary condition for k, and by linearity you see that it is also sufficient)