What is the basis of this vector space? Watch

Brian Moser
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What is the basis of the vector space V of the set of all polynomials p(x) of degree up to 3? So elements in this set would have the form p(x)=ax^{3}+bx^{2}+cx+d


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DFranklin
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No such thing as "the basis" for a vector space. There are lots (an infinite number!) of possible candidates.

That said if you express a general vector in terms of a basis x_0, x_1, ..., x_n you end up with something looking like: a_0 x_0 + a_1 x_1 + a_2 x_2 + ... + a_n x_n. Looking at your original post, does this suggest anything?
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