# Homework Help: (LinearAlgebra) If a vector space is given, how do I know if W is subspace or not?

1. Aug 4, 2011

### Sanglee

1. The problem statement, all variables and given/known data

Let V be the spcae of all 3x3 matrices with real entries. Is W, the set of all 3x3 lower triangular matrices, a subspace of V? Why or why not?

2. Relevant equations

3. The attempt at a solution

I just think that all 3x3 lower triangular matrices are included in all 3x3 matrices with real entires.
So my answer is that W is a subspace of V. but I don't know correct answer.
and I don't know how to explain why I think W is a subspace of V...
I think I'm missing an important definition or theorem...?

2. Aug 4, 2011

### vela

Staff Emeritus
Re: (LinearAlgebra) If a vector space is given, how do I know if W is subspace or not

That just means W is a subset of V.
You're missing the definition of a subspace. You need to understand that first. Then there's a theorem that tells you what you need to show to prove W is a subspace of V.