Hi I have two questions, I hope some one can help me.
Which subsets of the vector space Mnn are subspaces?
a) The set of all n x n symmetric matrices.
b) The set of all n x n diagonal matrices.
Thanks ^_^
all A where $\displaystyle A = A^T$ is the definition of your first subset. From there you need to prove that the summation of two elements from the subset results in an element of your subset and that any scalar multiplication also has the same result (definition of a subspace).
e.g. Can you prove that $\displaystyle (A+B) = (A+B)^T$ and $\displaystyle \alpha \cdot A = \alpha \cdot A^T$ where $\displaystyle A, B \in S_1; \alpha \in \Re$ ?