Question: 7. (5 points (bonus)) Two vector spaces V and W are isomorphic if there exist linear transformations T : V - W and S :

7. (5 points (bonus)) Two vector spaces V and W are

7. (5 points (bonus)) Two vector spaces V and W are isomorphic if there exist linear transformations T : V - W and S : W - V such that ST = ly and TS = Iw, where Iv and Iw are the identity operators on V and W respectively. Show that if V has dimension n, then V and R" are isomorphic. Hint: Pa

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