a) let T : R3 → R be a linear transformation defined by T(a, b, c) = 2a−b+ 5c. Find y ∈ R3 such that T(x) =< x, y > for all x ∈ R3 . b) Let T : V → V be a linear operator over a finite dimensional vector space V . Prove that dim(ker(T)) + dim(ImmT) = Dim(V )

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