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I'm still having a lot of trouble with this question: Defining a linear transformation

I don't understand how I can transform those vectors in a linear transformation and, besides that, I don't really understand the vector approach. Has anyone has other ideas on how to explore the problem?

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So the first thing to realise is that the whole space (V) is spanned by unit elements (which satisfy the axioms of a linear space), meaning any element of V can be made by adding together these unit elements. so to work out the solution to your problem, you need to define how each of these transformations act on the unit elements (which is the previous question are called $v$ and labeled with different letters). Try with this approach and see what happens. Don't worry about vectors and matrices, while they are the most used and essential linear objects, they do not need to be though of explicitly.

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  • $\begingroup$ Hey! The problem I guess is that I'm making wrong conclusions: I'm thinking that the elements that only belong to U have F(x) = S(x) and the ones that belong only to W have F(x) = T(x). Then I have the problem of those who belong to both U and W... $\endgroup$ Apr 25, 2016 at 16:55
  • $\begingroup$ But I'm probably making wrong assumptions $\endgroup$ Apr 25, 2016 at 16:55

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