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determine whether the given function is a linear transformation by showing proofs. T:P2->P2, defined by

T(p(x))= p'(x)+x^2 (P2 means polynomial 2 p'(x) means derivative of p x^2 means x squared)

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Let p(x) and q (x) be two polynomials ∈ P2 , then
T (a.p(x) + b.q (x)) = d
(a.p(x) + bq (x)) + x2
dx = a.p (x) + b.q (x) + x2
On the other hand we have
a.T (p(x)) + b.T (q (x)) = a.p (x) + bq (x)...

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