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Let Mn be the vector space of all n × n matrices with real entries. Let...

Let Mn be the vector space of all n × n matrices with real entries. Let W = {A ∈ M3 : trace(A) = 0}, U = {B ∈ Mn : B = B t } Verify U, W are subspaces . Find a basis for W and U and compute dim(W) and dim(U).

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