Exercise 1.3.11

Question

Is the set $\mathrm{W}=\{f(x) \in \mathrm{P}(F): f(x)=0$ or $f(x)$ has degree $n\}$ a subspace of $\mathrm{P}(F)$ if $n \geq 1$ ? Justify your answer.

Jephian C.-H. Lin · Accepted Answer

No in general but Yes when $n=1$. Since $W$ is not closed under addition. For example, when $n=2$, $(x^2+x)+(-x^2)=x$ is not in $W$.

Exercise 1.3.11

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Exercise 1.3.11

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