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Mathematics 13 Online
OpenStudy (anonymous):

help! Let F be a field, and let n be a positive integer. For any A ∈ Mn×n(F), the trace of A, tr(A), is defined to be the sum of the diagonal entries of A; that is, tr(A) = Pn i=1 A(i, i). Let W = {A ∈ Mn×n(F) | tr(A) = 0 }. a)Find a basis for W, and determine the dimension of W.

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