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A Peculiar Set of Linear Equations

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

It is easily seen that each of the equations of the set

remains unaltered for each of the three interchanges

and that the set as a whole is not altered by the simultaneous performance of the cyclical substitutions

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 23 , 1902 , pp. 248 - 260
Copyright
Copyright © Royal Society of Edinburgh 1902

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References

* The peculiar set of equations dealt with in this short paper can scarcely have escaped notice until now. They were suggested to me while examining a problem set by Professor Nanson in the Educational Times for September 1900, viz., “If a=(x2 – y)/(1 – xy), and b=(y2 – x)/(1 – xy), prove that (a2 – b)/(1 – ab) = x and (b2 – a)/(1 – ab) = y.”