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A set of three numbers {a, b, c} is given. We are allowed to transform it...

A set of three numbers {a, b, c} is given. We are allowed to transform it in the following way: pick any two of them, say a and b, and replace them with two numbers (√ 3 a + b)/2 and (−a + √ 3 b)/2. Is it possible to obtain the triple {2, − √ 3, 1 − √ 3} from the triple {2, √ 3, √ 3/3} by performing a sequence of such operations? Justify your answer.

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