Symmetric Matrix as a subspace

[seyma]

My question is;
Let S = {A € Mn,n | A = AT } the set of all symmetric n × n matrices
Show that S is a subspace of the vector space Mn,n

I do not know how to start to this if you can give me a clue for starting, I appreciate.

 

[Vid]

What are the conditions that a subset be a subspace? It's not hard to show that S satisfies them.

 

[seyma]

edit: A=A^T

It must satisfies the operations in S and it requires that it must be closed under vector addition and scaler multiplication. I got it: symmetic matrix satisfies those condition :) thanks:)