i'd be extremely grateful if anyone can help me out with this
Suppose V is a ﬁnite dimensional inner product space and T : V → V a linear operator.
1. Prove im(T∗ ) = (kerT )⊥.
2. Prove rank(T ) = rank(T∗ ).
T∗ should be displayed as T^*, as is (kerT )⊥ should be (kerT)^⊥