The set of all polynomials of degree greater than three together with the zero polynomial in the vector space $P$ of all polynomials with coefficients in $\Bbb{R}$.
I thought I understood generally how to do this but my book (Linear Algebra: Fraleigh, Beauregard, Wesley 1995) explains how to determine whether the subset is a subspace of the vector space. It seems like it already assumes the set is a subset.
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How do I determine if a set is a subset of a vector space? Is it with the 8 axioms of vector addition and scalar multiplication?
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How do I read this problem specifically? I'm not really sure how to write these out in set notation.
This isn't homework perse. I am studying for my final tomorrow though.
Best Answer
To check that a subset is a subspace you need to check three axioms:
1.Closed under addition
2.Closed under scalar multiplication
3.Non empty
In your case is very simple since $deg((x^3+1)+(-x^3))=deg(1) <3$