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(a) Consider x^2 + 7x + 15 = f(x) and e^x = g(x) which are vectors...

(a) Consider x^2 + 7x + 15 = f(x) and e^x = g(x) which are vectors of F(R, R) with the usual addition and scalar multiplication. Are these functions linearly independent?

(b) Let S be a finite set of linearly independent vectors {u1, u2, · · · , un} over the field Z2. How many vectors are in Span(S)?

(c) Is it possible to find three linearly dependent vectors in R^3 such that any two of the three are not linearly dependent themselves?

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