Question: If A is a symmetric matrix and a numerically stable algorithm is used to compute the eigenvalues of Ax = b, then the relative error

If A is a symmetric matrix and a numerically stable algorithm is used to compute the eigenvalues of Ax = b, then the relative error in the computed eigenvalues should always be small.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.

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