0
$\begingroup$

I have been fuzzy on this transformation stuff and am practicing for an upcoming test.

 Find the standard matrix: counterclockwise rotation through 60 degrees, followed by a reflection in the line y=x

I am not exactly sure how to do this. My textbook gives an example of how to find the standard matrix of a rotation by a formula. I also know that the standard matrix of a reflection of the line y=x is {{0,1},{1,0}}. But, I don't really know how to tackle this problem.

Thanks

$\endgroup$
1
$\begingroup$

Hint: The column vectors of the linear transformation matrix will be wherever the standard basis vectors are mapped to.

$\endgroup$
  • $\begingroup$ Hmm, I don't know how I should put that statement in action $\endgroup$ – A A Apr 6 '14 at 1:14
  • $\begingroup$ where the standard basis vectors are mapped to. What does this mean? $\endgroup$ – A A Apr 6 '14 at 1:17
  • $\begingroup$ The vector $<1, 0>$, our first standard basis vector, gets rotated $60$ degrees, so it becomes $<.5, \frac{\sqrt{3}}{2}>$. Next, it gets reflected over the line $y=x$. In other words, the $x$ coordinate becomes the $y$-coordinate and vice versa. So we get $<\frac{\sqrt{3}}{2}, .5>$. This is therefore the first column vector in our matrix. For the second column in our matrix, you'll have to find where the second standard basis vector, $<0, 1>$, gets mapped to. $\endgroup$ – Kaj Hansen Apr 6 '14 at 1:17
  • $\begingroup$ So the other column vector should be <0.5, sqrt(3)/2>, right? $\endgroup$ – A A Apr 6 '14 at 1:22
  • $\begingroup$ I have used your method and the matrix should be {{sqrt(3)/2,0.5},{0.5,sqrt(3)/2}} $\endgroup$ – A A Apr 6 '14 at 1:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.