Question: 8. [15 points] Define T : P3(R) - M2(IR) by T(f) = f'(0) 2f(1) 0 f (2 ) (a) Show that T is a linear

8. [15 points] Define T : P3(R) - M2(IR) by T(f)

8. [15 points] Define T : P3(R) - M2(IR) by T(f) = f'(0) 2f(1) 0 f" (2 ) (a) Show that T is a linear transformation. (b) Find bases for ker(T) and range(T). (c) Compute the nullity and rank of T and verify the Dimension Theorem (rank equation)

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