Is the Set of Lower Triangular Matrices a Subspace of 3x3 Matrices?

[Sanglee]

Homework Statement

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?

Homework Equations

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...?

 

[vela]

I just think that all 3x3 lower triangular matrices are included in all 3x3 matrices with real entires.

That just means W is a subset of V.

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...?

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.