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 Mentor P: 18,027 Linear transformations - Proving that a set generates the targe space OK, that's good. I'll also assume that you're working with $$\mathbb{R}$$ vector spaces, not that it matters a lot... Now consider the vector space $$E=\mathbb{R}^X$$. Can you find a basis for this vector space? Can you find an easy linear transformation f:E-->F??