# Homework Help: Proving W is a subspace.

1. Sep 19, 2013

### dylanhouse

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

Given W={A belonging to M2(ℂ) | A is symmetric} is a subspace of M2(ℂ) over ℂ, when showing it is closed under scalar multiplication, do I need to use a complex scalar as it is over the complex numbers, or will a real number be okay?

2. Relevant equations

3. The attempt at a solution

2. Sep 19, 2013

### kostas230

You have to prove that it's closed under scalar multiplication using complex numbers, as the vector space $M_2(\mathbb{C})$ is a vector space over the complex numbers.