Problem 5. Recall that Mn,n(R) is the vector space of all n by n real matrices....

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.?

Expert Solution

we use basic properties of trace

Colby Messinger answered 6 months ago

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