Pet P4 be the set of all polynomials of degree less than four.
Is the set S of polynomials of even degree less than four a subspace of P4?
I think that it is; however my text says it isn't.
Here's why I think that it is.
let v be an element of the Set described. Then v is an even degree polynomial of deg less than four. If we take a scaler œ and multiply v by it, we get another polynomial of the same deg before. So, œv is in S. Satisfying closure one.
Let v,x be in S, then consider v+x v+x is a polynomial with the highest even degree between them, and this will be less than 4, and it will be even. So, v+x is in S.
What did I do wrong, if anything?