If anyone could help me with this problem it would be great. I am very lost on this. Thanks.. In trying to figure this out, I learned that 
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2026-03-25 11:25:34.1774437934
Perturbation of matrix proof
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Hint: Note that $\delta \mathbf x = A^{-1}\;\delta \mathbf b$, so that $$ \|\delta \mathbf x\| = \|A^{-1}(\delta\mathbf b)\| \leq \|A^{-1}\|\|\delta \mathbf b\|\\ \|\mathbf b\| = \|A \mathbf x\| \leq \|A\| \|\mathbf x\| \implies \|\mathbf x \| \geq \frac{\|\mathbf b\|}{\|A\|} $$