
subspace test
Let A be an n×n matrix and let W = {v ∈ RnAv = 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.

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?