# Thread: Is the set a subspace?

1. ## Is the set a subspace?

(apology on the format; I don't know the beginning format for latex)

Is the set W={p (epsilon) C2(-infinity, infinity) | 4p''-6p'+2p=0} a subspace of P2(-inf,inf) with the normal operations of polynomial addition and scalar multiplication?

Can someone give me some advice on how to start?

2. ## Re: Is the set a subspace?

Could you remind what P2(-inf,inf) is?

The question seems to ask whether the sum of two solutions of 4p''-6p'+2p=0 is again a solution. Well, differentiation is a linear operator...

3. ## Re: Is the set a subspace?

would W be a subset because P2 contains all real numbers?

I don't follow where you get the sum of two solutions.

4. ## Re: Is the set a subspace?

I am still not sure what P2(-inf,inf) is.

WolframAlpha says that the solutions to 4p''-6p'+2p=0 are $c_1e^{x/2}+c_2e^x$ for various $c_1,c_2$. These are not polynomials unless $c_1=c_2=0$.

What I meant is that as a subset of C2(-infinity, infinity), W is a vector space, i..e., it is closed under addition and scalar multiplication. That's why I said that the sum of two solutions is again a solution.