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Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I...

Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I ∈ L(R2) be the identity operator.
Using the inner product defined in problem 1 for the standard basis and the dot product,
compute <S, I>, || S ||, and || I ||

{Inner product in problem 1: Let W be an inner product space and v1, . . . , vn a basis of V. Show that <S, T> = <Sv1, T v1> + . . . + <Svn, T vn> for S, T ∈ L(V, W) is an inner product on L(V,W).}

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