Findalllinear transformations T: R^{2 }--> R^{2}which carry the line y=x to y=3x.

Please help

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- Apr 22nd 2013, 08:44 AMarindamnaskrProblem on Linear Transformations
Find

__all__linear transformations T: R^{2 }--> R^{2}which carry the line y=x to y=3x.

Please help - Apr 22nd 2013, 06:55 PMchiroRe: Problem on Linear Transformations
Hey arindamnaskr.

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. - Apr 23rd 2013, 05:26 AMarindamnaskrRe: Problem on Linear Transformations
:) 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. - Apr 23rd 2013, 07:57 AMHallsofIvyRe: Problem on Linear Transformations
The angle between the two lines is $\displaystyle \theta- \phi$ where $\displaystyle tan(\theta)= 3$ and $\displaystyle tan(\phi)= 1$, the slopes of the two lines. And

$\displaystyle tan(\theta- \phi)= \frac{tan(\theta)- tan(\phi)}{1+ tan(\theta)tan(\phi)}$ - Apr 23rd 2013, 08:36 AMarindamnaskrRe: Problem on Linear Transformations
- Apr 23rd 2013, 02:16 PMHartlwRe: Problem on Linear Transformations