subspace 3: prove symm., anti-symm. matrices are subspaces

[Apprentice123]

Prove that the set S1 of symmetric matrices and the set S2 the anti-symmetric matrices nxn are vector subspaces of the Mnxm and that it has Mnxm = S1 + S2

 

[tkhunny]

Re: subspace 3

Define subspace. Feel free to take a shot at the proof.