Question

Having two subspaces:

Answer 1

\[S1 = [ A=((a_{ij})) \in R^{3x3} / a_{ij} =0 \leftarrow \rightarrow i+j --- is--- pair]\]
\[S2 = [B=((b_{ij})) \in R^{3x3} / b_{ij} = - b_{ji} \forall (i,j) ]\]

a) Find the dimension of the subspace S1
b) Find the orthogonal complement
c) Find S3 = S1 ∩ S2. S3 is a subspace?