Prove that S + T and cT are linear transformations.
The set of all linear transformations from a vector space V to a vector space W is denoted by £(V, W) . If S and T are in £ (V, W), we can define the sum S + T of S and T by
(S + T) (v) = S(v) + T(v)
for all v in V If c is a scalar, we define the scalar multiple cT of T by c to be
(cT) (v) = cT(v)
for all v in V Then S + T and cT are both transformations from V to W