1. subspace test

Let A be an n×n matrix and let W = {v ∈ Rn|Av = 2v} . Is W a subspace of Rn?
I don't know how to prove it using the subspace test.

I know that W is a subspace of Rn.

I tried saying that the 0 vector is a element of W since v is a element of Rn. Av = 2v

How do you do the addition and scalar multiplication?

Never mind.. I figured it out.

2. Re: subspace test

all you have to do is verify closure under vector addition and scalar multiplication (since you've already covered the additional requirement that 0 is in W).

so suppose u,v are in W. is u+v in W? if c is any scalar (real number, in this case), is cu in W?