In this paper we discuss here linear Transformation and operators and illustrate the definition with an example. Let V and W be a vector space over the field F let T and U be the linear transformation from V into W. The function (T+U) defined by. (T+U)(V)=TV+UV Is a linear transformation from V into W let SEF the function (ST) defined by (ST) (V)= S(TV) Is also linear transformation from V to W the set of all linear transformation from V into W[, together in the addition and scalar transformation defined a some is a vector space over the field. Proof: Let T and U are the linear transformation from V into W then (T+U)(SV+W)=T(SV+W)+U(SV+W) = S(TV)+TW +S(UV)+UW) = S(TV+UV)+(TW+UW) = S(T+U)V+(T+U)W Which shows that (T+U) is a linear transformation. Similarly we have (rT) (SV+W)=r (T(SV+W) ) =r(S(TV)+ T(W) ) =rS(TV)+r (TW) =S(r (TV) )+rT(W) =S( (rT)V)+ (rT)W Which shows that (rT) is a linear transformation.