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Question Number 167839 by mathlove last updated on 27/Mar/22

Answered by mr W last updated on 27/Mar/22

$$sayx+y+z-3=s$$$$\Rightarrow x+y+z-s=3$$$$\left[\begin{array}{cccc}\frac{1}{668}& \frac{1}{669}& \frac{1}{670}& 0\\ \frac{1}{670}& \frac{1}{671}& \frac{1}{672}& 0\\ \frac{1}{674}& \frac{1}{675}& \frac{1}{676}& 0\\ 1& 1& 1& -1\end{array}\right]\left(\begin{array}{c}x\\ y\\ z\\ s\end{array}\right)=\left(\begin{array}{c}1\\ 1\\ 1\\ 3\end{array}\right)$$$$s=\left[\begin{array}{cccc}\frac{1}{668}& \frac{1}{669}& \frac{1}{670}& 1\\ \frac{1}{670}& \frac{1}{671}& \frac{1}{672}& 1\\ \frac{1}{674}& \frac{1}{675}& \frac{1}{676}& 1\\ 1& 1& 1& 3\end{array}\right]/\left[\begin{array}{cccc}\frac{1}{668}& \frac{1}{669}& \frac{1}{670}& 0\\ \frac{1}{670}& \frac{1}{671}& \frac{1}{672}& 0\\ \frac{1}{674}& \frac{1}{675}& \frac{1}{676}& 0\\ 1& 1& 1& -1\end{array}\right]=2012$$

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