Question: Please help me solve this question. Thank you! . Let T : R2 > R2 be the linear transformation that is rotation counterclockwise by 71'

Please help me solve this question. Thank you!

. Let T : R2 > R2 be the linear transformation that is rotation counterclockwise by 71' / 2 (90 degrees). Let S : R2 > R2 be projection onto the the xaxis. This means that S (x) = x for any vector x in the xaxis, and S'(x) = 0 for any vector perpendicular (normal) to the maxis. You do not need to nd formulas for T and S to do this problem. Thinking geomet rically and / or drawing the linear transformation may be helpful. (a) Find all eigenvalues and eigenvectors of T. Explain, using a picture of the unit square to guide you. (b) Find all eigenvalues and eigenvectors of 8. Explain, using a picture of the unit square to guide you. (c) Find one eigenvalue of S o T and give an example of one eigenvector with that eigenvalue. Explain, using a picture of the unit square to guide you. Remember that S o T(x) = S(T(x))

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