let v be the set of all 2x2 matrices a with complex entries

let v be the set of all 2x2 matrices a with complex entries which satisfy An + An = 0. let W be the set of all matrices A in V such that An = - An. Prove that W is a subspace of V and find a basis for W.

Solution

f W is a subset of a vector space V and under the operations \"+\" and \".\" of V , W itself is a vector space, we call W a vector subspace or just a subspace ofV . It is obvious that W is a subspace of V iff W is closed under the operations \"+\" and \"-\" of V .