Let

L(V,W)

be the set of linear transformations from

V

to

W

. Prove that the set

L(V,W)

forms a vector space using the following operators. Let

S,TinL(V,W)

and

cinF

\

(ST)(v)=S(v)o+T(v)\ (cT)(v)=co.T(v)

\ where

o+

is the vector addition operator from

W

and

o.

is the scalar multiplications operators from

W

. (Remember to show closed under addition and multiplication.) Suppose,

V

and

W

are both finite dimensional, determine the dimension of

L(V,W)

.

Let L(V,W) be the set of linear transformations from V to W. Prove that the set L(V,W) forms a vector space using the following operators. Let S,TL(V,W) and cF (ST)(v)=S(v)T(v)(cT)(v)=cT(v) where is the vector addition operator from W and is the scalar multiplications operators from W. (Remember to show closed under addition and multiplication.) Suppose, V and W are both finite dimensional, determine the dimension of L(V,W)