Let (A, B in mathbb{R}^{n times n}) be symmetric matrices. If (langle A x, xangle=langle B x,

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Let \(A, B \in \mathbb{R}^{n \times n}\) be symmetric matrices. If \(\langle A x, xangle=\langle B x, xangle\) for all \(x \in \mathbb{R}^{n}\), then \(A=B\).

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