Hint: Consider a rotation matrix taking a point on the line y = x to y = 3x by considering rotating both points by the difference of the angle between the two lines.
yes... I thought about that...but, the problem with that approach is finding the angle between those two lines...i mean, the angle is not something nice. So, I have been looking for an approach in which the matrix of T looks nice.
Anyway, thank you for the reply. Please let me know if you come up with another approach.
Find all linear transformations T: R2 --> R2 which carry the line y=x to y=3x.
Take a point x,y on l1 and draw a line l through it with slope m. The intersection of l with l2 represents a linear transformation of l1 to l2 for arbitrary m (all linear transformations from l1 to l2). Then solve