2. For each of the following linear operators T on a vector space V, test T for diagonalizability. If T is diagonalizable, find a basis for V such that B[T] is a diagonal matrix, and write down the matrix B[T]B. (a) T : P3(R) → P3(R) defined by T(ƒ) = f' + ƒ" ([₁]) = [z+iw] iz + w (Note: Here we are thinking of C² as a 2-dimensional vector space over C, as usual. So z and w represent complex numbers, not real numbers.) (b) T : C² ⇒ C² defined by T

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A: note : Since you have posted multiple questions, we will provide the solution only to the first…