1. ## subspaces

Let V be the usual real vector space of all 3 x 3 real matrices. Define subsets of V by
U = { A is in V : A^T= A } and W = { Ais in V : A^T= -A }
Show that both U and W are subspaces of V.

2. $0\in U$ and for $A,B\in U$
$(A+B)^T=A^T+B^T=A+B$
and
$(cA)^T=cA^T=cA$
So $A+B\in U$ and $cA \in U$.

Do the same for V