Prove that , the set of all real nxn matrices formsa vector space over R of dimension . Determine which of the following subsetsof are subspaces and (when possible) find abasis for the subspace and determine the dimension.

(a)The set of all diagonal matrices A with for .

(b)The set of all matrices A with detA=0

(c)The set of all upper triangular matrices A with

(d)The set of all matrices with traceA=0


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