(Solution Library) Suppose that V is a real inner product space, with inner product and norm \|v|=√>. Prove the Parallelogram Law, which
Question: Suppose that \(V\) is a real inner product space, with inner product \(\langle-,-\rangle\) and norm \(\|\mathbf{v}\|=\sqrt{\langle\mathbf{v}, \mathbf{v}\rangle}\rangle\). Prove the Parallelogram Law, which says that
\[\|\mathbf{u}+\mathrm{v}\|^{2}+\|\mathbf{u}-\mathrm{v}\|^{2}=2\|\mathbf{u}\|^{2}+2\|\mathbf{v}\|^{2}, \quad \text { for all } \mathbf{u} \text { and } \mathbf{v} \text { in } V\]
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