Please see problem #1 of the attachment. If you show me how to do #1 (the answers are a and d, by the way) I'll probably be able to do #2.
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Please see attachment.
By definition, vectors I and J form an orthonormal basis in R2 when ITI = JTJ = 1
and JTI = ITJ = 0 ...
This shows how to find an orthonormal basis.