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June 13th, 2013, 08:08 PM   #1
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Problem with matrices.

Hi, hi!

I'd like you help with the two following problems:

(a) Verify that the 2 x 2 matrix is an orthogonal matrix.
(b) Let T be the linear transformation with the above matrix A relative to the usual basis {i,i}. Prove that T maps each point in the plane with polar coordinates onto the point with polar coordinates . Thus, T is a rotation of the plane about the origin, 0 being the angle of rotation.

I don't have any problem with a). But I not sure how to prove the second.

┐How do I prove the relation of a transformation with its geometric interpretation?
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June 16th, 2013, 12:03 PM   #2
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Re: Problem with matrices.

The point with polar coordinates has Cartesian coordinate . Multiply that by the given matrix. You will need the trig identities and .
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