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_{n}(k) be a vector space of matrices with entries in k. For a matrix M denote the trace of M by tr(M).

What is the dimension of the subspace of {M[tex]\in[/tex]V: tr(M)=0}

I know that I am supposed to use the rank-nullity theorem. However I'm not sure exactly how to use it. I know that the trace is a linear map itself. Since in this case it equals zero would the dim=dim(ker)?