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# Let T be the set of all real 2x2 matrices with zero trace: T = {A â‚¬ Mz(R) tr( A) = 0} a) Prove that T is subspace of V Mz(R). (b) Construct a basis for T. Pro...

## Question

###### Let T be the set of all real 2x2 matrices with zero trace: T = {A â‚¬ Mz(R) tr( A) = 0} a) Prove that T is subspace of V Mz(R). (b) Construct a basis for T. Prove that your collection does in fact form a basis Hint: You need to decide what typical element of T looks like. What has to be true about the entries along the main diagonal of A for tr(A) = 0?)

Let T be the set of all real 2x2 matrices with zero trace: T = {A â‚¬ Mz(R) tr( A) = 0} a) Prove that T is subspace of V Mz(R). (b) Construct a basis for T. Prove that your collection does in fact form a basis Hint: You need to decide what typical element of T looks like. What has to be true about the entries along the main diagonal of A for tr(A) = 0?)

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