1. ## Subspace

Hi,

$n \in \mathbb{N}*$ and D is the set of polynomials.
How to show that the following sets are not a vector subspaces:

2. Originally Posted by bhitroofen01
Hi,

$n \in \mathbb{N}*$ and D is the set of polynomials.
How to show that the following sets are not a vector subspaces:

So, you need to show that they do not withhold the subspace axioms.

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1. What conditions would these sets need to fill in order to be vector subspaces?

2. Now that you've answered q1, it should be easy to find an example (even the same example for all three of them) that shows they are not subspaces.

3. i know that is hould show $\exists P_1,P_2\in E:\alpha_1 P_1 + \alpha_2 P_2 \notin E$, but how to do it?? Can you do just a one example???

4. Originally Posted by bhitroofen01
i know that is hould show $\exists P_1,P_2\in E:\alpha_1 P_1 + \alpha_2 P_2 \notin E$, but how to do it?? Can you do just a one example???
I'll give you a hint. There is one example that works for all of them, and it is very simple. You do not even need to give a specific polynomial. Think about it this way: Say you are given some polynomial $p(x) \in E_1$. How can you change $p(x)$, to get $q(x)$ such that $p(x) + q(x) \notin E_1$?