Let T be the transform from P2 the vector space of second de

Let T be the transform from P2 (the vector space of second degree polynomials) into 3 defined by, T(p(t)) = [p(1) p(2) p(3)](where the prime denotes the derivative.) Show that T is a linear transformation. Is T an isomorphism

Solution

T(p(t))= [p(1), p(2), p(3)]

we have to show that T is linear tranformation

so

T(p(t)+kQ(t)) = [p(1), p(2), p(3)] + k [Q(1), Q(2), Q(3)]

hence T is linear tranformation