For n a positive integer prove that Vn and LFn V are isomorp

For n, a positive integer, prove that Vⁿ and L(Fⁿ, V) are isomorphic vector spaces.

Solution

For n, a positive integer={1,2,3,4,5,-------n}

prove that V_n and L(Fn, V) are isomorphic vector spaces.

if fn is some function it varry according to n values

      and V also change,

so,

for every n-value fn,vn is different values.

like if fn=(x²,vx)

            then fn={(1,1),(4,2),(9,3)----------(n²,n)}

    so we say this is isomorphic vector spaces according to definition.

A function f:X->Y is a one-to-one correspodence between X and Y if, for each y in Y,

            there is exact one solution in X total equation is

                      f(x)=y.