Asymmetric replacement

Start with the set \(\{2, 3, 4\}\). In each step, choose two numbers \(a\) and \(b\), and replace them with \(0.6a-0.8b\) and \(0.8a+0.6b\).

(a) Is it possible to reach the set \(\{1, 3, 5\}\)?
(b) Is it possible to reach the set \(\{0, 2, 5\}\)?

(adapted from Engel, Problem Solving Strategies, p.9)

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