7. Theorem : Let V and W be vector spaces over a field F. Let {v1,.., vn} be a basis of V and let w1,..., wn be any arbitrary vectors in W. Then there exists a unique linear transformation F : V → W such that F(v1) = w1, . .. , F(vn) = wn. a. Using the Theorem, show that there is a unique linear transformation F : R? → R² for which F(1,2) = (2,3) and F(0, 1) = (1, 4). b. Find a formula for F i.e find F(a,b). c. Find F(5,6).

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Q: (a) Let V = F[x] be the vector space of polynomials over a field F. Show that the set S = {1, x, x²,…

A: As per our company guidelines we have solve only one question. Kindly repost other part in next…

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