Proof or counterexample. Here \(v, w, z\) are vectors in a real inner product space \(H\).

a) Let \(v, w, z\) be vectors in a real inner product space. If \(\langle v, w\rangle=0\) and \(\langle v, z\rangle=0\), then \(\langle w, z\rangle=0\).

b) If \(\langle v, z\rangle=\langle w, z\rangle\) for all \(z \in H\), then \(v=w .\)

c) If \(A\) is an \(n \times n\) symmetric matrix then \(A\) is invertible.