In: Advanced Math
Problem 5. Recall that Mn,n(R) is the vector space of all n by n real matrices.
(a) Show that W = {A | tr(A) = 0} is a subspace of Mn,n(R).?
(b) Determine the dimension of W and find a basis for it.?
(c) Show that the trace map tr : Mn,n(R) → R is a linear transformation.?