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

Please help

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- April 22nd 2013, 09:44 AMarindamnaskrProblem on Linear Transformations
Find

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

Please help - April 22nd 2013, 07:55 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. - April 23rd 2013, 06:26 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. - April 23rd 2013, 08:57 AMHallsofIvyRe: Problem on Linear Transformations
The angle between the two lines is where and , the slopes of the two lines. And

- April 23rd 2013, 09:36 AMarindamnaskrRe: Problem on Linear Transformations
- April 23rd 2013, 03:16 PMHartlwRe: Problem on Linear Transformations