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Together and Alone Problem : Solve by Matrix Methods

Four friends (Gauss, Euler, Cramer, and Einstein) can solve a 20 variable system in 11 hours. Gauss, Euler and Cramer can do it in 18 hours, while Euler, Cramer and Einstein take 16 hours. Gauss, Euler and Einstein can do it together in 14 hours. Define variables, set up a system, and using matrices, determine how long it takes Cramer to finish the problem by himself. You may use whatever strategy you wish, but clearly state which method you are using.

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Further clarification from OTA:

"I don't follow how you got the initial four equations 1/x + 1/y etc. I am not familiar with the adjoint method. Please ...

Solution Summary

A "together and alone problem" is solved by matrix methods.