Good method for checking solutions to linear systems of equations by hand

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SUMMARY

The discussion focuses on effective methods for verifying solutions to linear systems of equations, particularly those encountered in first-year university linear algebra courses. The primary technique mentioned is the use of Gauss/Gauss-Jordan elimination, which simplifies the checking process when solutions are free of arbitrary scalars. For solutions involving parameters, such as x1=5 + 4t + 3s, participants suggest inserting answers back into the original equations to ensure consistency. This method becomes increasingly efficient as the complexity of the system grows.

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  • Understanding of Gauss/Gauss-Jordan elimination
  • Familiarity with linear systems of equations
  • Basic knowledge of parameterized solutions in linear algebra
  • Ability to manipulate and substitute equations
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Hello all,

I was wondering if any of you have a good method for checking your answers to linear systems of equations(when working by hand).
I mean the sorts of equations you would encounter on a first university linear algebra course. I solve the system with Gauss/Gauss-Jordan elimination, and if my solution has no arbitrary scalars then it is easy enough to check.
However if my solutions is along the lines of:
x1=5 + 4t + 3s
etc, then it becomes much harder to check.

Any techniques you use to check your answers, and to avoid mistakes in the first place, when you are working quickly by hand would be appreciated.

Thanks
 
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Just add all your equations and insert your answers and see if it checks in total. As the system of equations grows, this short cut gets progressively more effective.

It would be unlikely if you happen to have offsetting errors.
 
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