Elementary Linear Algebra

When it comes to linear algebra, we can even think of the polynomials as "vectors". Consider the transformation which takes real-valued polynomials of at most order 3 in z and maps them to their derivative, T : P3(R) - P?(R) by, T(p(=)) - p'(=). for a polynomial of order 3, p(z). For example, the polynomial r(z) = 32 + 22 + z + 1 is mapped as follows: d T(r) = dz (323 + 2z* + z + 1) = 92~+ 4z+1. Show that T is a linear transformation