Let n 1 be an integer and W= {AM_n(R): Tr(A)M_n(R)}

Show that W is a subspace, and find a subspace V M_n(R) such that M_n(R) = V W. Hint: The dimension (to be made precise next week) of M_n(R) is n^2 and the dimension of W is

n^2 1. Also, don't forget the powerful magic of adding zero.

note: here is the question in image if the formatting is bad

https://imgur.com/a/DklhyJs