Question: Consider the transformation T: mathbb{P}_3 to mathbb{P}_3 defined by T(f(t))= 3 f^{prime}(t) + 2f(t) + 5 Is the transformation linear? Hint: Recall that a linear

Consider the transformation T: \mathbb{P}_3 \to \mathbb{P}_3 defined by T(f(t))= 3 f^{\prime}(t) + 2f(t) + 5 Is the transformation linear? Hint: Recall that a linear transformation must map the zero "vector" into the zero "vector". If f(t) =0, what is T(f(t))

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