Question: 3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as

3. Determine if the mappings T and S specified below are linear transformations. Do this by verifying the defining properties, or giving a counterexample, as appropriate. (a) T : M2,2 - R defined by T a b C d = ad - bc.(b) S : P2 + P3 defined by S(p(x)) = xp(x) + Ap(x).(c) In the case of S, calculate the standard matrix representation

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