mooshupork34

04-30-2007, 10:37 PM

If anyone could explain how the following problem on linear transformations is done, it would be greatly appreciated!

There is a theorem that assures us that if L: V->W is a linear transformation, then L(av_1 + bv_2) = aL(v_1)+bL(v_2), for all v1, v2 in V and all a, b in R. Prove that the converse of this statement is true by considering two cases: first a=b=1 and then b=0.

There is a theorem that assures us that if L: V->W is a linear transformation, then L(av_1 + bv_2) = aL(v_1)+bL(v_2), for all v1, v2 in V and all a, b in R. Prove that the converse of this statement is true by considering two cases: first a=b=1 and then b=0.