Let V be the Euclidean space of all 2 x 2 matrices with inner product defined by

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Let V be the Euclidean space of all 2 x 2 matrices with inner product defined by (A, B) = Tr(BT A).
(a) Prove that
Let V be the Euclidean space of all 2 x

Is an orthonormal basis for V.
(b) Use Theorem 5.5 to find the coordinate vector of

Let V be the Euclidean space of all 2 x

With respect to S

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