Find all linear transformations T: R^{2 }--> R^{2} which carry the line y=x to y=3x.
Please help
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.
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
$\displaystyle tan(\theta- \phi)= \frac{tan(\theta)- tan(\phi)}{1+ tan(\theta)tan(\phi)}$