1) Any fuction T: V->W . V and W are vector spaces over the field of rational numbers. The fuction T is called additive if T(x+y)=T(x)+ T(y). Proof that any function T from v to w are additive, then it must be a linear transformation. 2) Let T:V->W be linear prove that if T is 1 to 1 IFF T carries linear indep subset in V to Linear, indep subset in W.