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1a) Determine whether this subset of C(R) is linearly independent or not; the dimension of the subspace and its basis

S=(e^ax, x*e^ax, x^2*e^ax)

this question seems to be too easy, they seem independent to me for obvious reasons. adn those 3 elements are the basis, and the dimension is then obviously 3. or am i wrong somewhere?

and it asks to show that one can find arbitrarily large finite sets of independent functions in C(R). then i take it x, x^2, x^3, etc are independent, now how do i show/prove this?

thanks!

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# Hw Help- Linear Algebra

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