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So assuming u=(cos x, sin x), where x is theta of course, is the direction of a line through (0,0) in R^2. And T is the operator which reflects vectors about the line. Using T(e1) and T(e2), How would I find the standard matrix for the transformation?

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  • $\begingroup$ Draw a picture. $\endgroup$
    – user137731
    Mar 28, 2016 at 0:43
  • $\begingroup$ As the problem suggests, find where the two unit vectors (0,1) and (1,0) end up and then build the matrix from that (the matrix is literally the transformation of the unit vectors). $\endgroup$
    – user2469
    Mar 28, 2016 at 4:07

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