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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.
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