S.O.S. Mathematics CyberBoard

two linear spaces S and S1 over F are isomorphic if and only if there is a one-to-one
correspondence x to x1 between the elements x belong to S and x1 belongs to S1
such that if x to x1 and y to y1 then x+y to x1+y1 and ax to ax1
(y belong S , y1 belong to S1, a belong F).
prove that two finite -dimensional spaces are isomorphic if and only if they are of the same dimension.
(The correspondence or mapping defining isomorphic linear spaces is called an
isomorphism).

please can you solve this question , really i have an exam, and i need your help.

You map a basis for to a basis for

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