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Find an inner product such that the vectors ( −1, 2 )T and ( 1, 2...

Find an inner product such that the vectors ( −1, 2 )T and ( 1, 2 )T form an orthonormal basis of R2

2

4.1.11. Prove that every orthonormal basis of R2 under the standard dot product has the form u1 =

cos θ

sin θ

and u2 = ±

− sin θ

cos θ

for some 0 ≤ θ < 2π and some choice of ± sign.

.

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