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

In summary, the conversation is about finding a good method for checking answers to linear systems of equations, specifically those encountered in a first university linear algebra course. The speaker uses Gauss/Gauss-Jordan elimination to solve the system, but mentions difficulty in checking solutions with arbitrary scalars. They ask for techniques to check answers and avoid mistakes when working quickly by hand. One suggestion is to add all equations and insert answers to see if it checks. It is also suggested to trust in Linear Algebra to avoid errors.
  • #1
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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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  • #2
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.
 
  • #3
Don't believe in yourself, believe in Linear Algebra who believes in you!
 

1. How do I know if my solution to a linear system of equations is correct?

The best way to check the solution to a linear system of equations by hand is to substitute the values of the variables into each equation and see if it satisfies all of them. If all the equations are satisfied, then the solution is correct.

2. Can I use a calculator to check my solution to a linear system of equations?

While calculators can be helpful in solving linear systems of equations, they should not be solely relied upon for checking the solution. It is important to manually check the solution by substituting the values and verifying that all equations are satisfied.

3. What are some common mistakes to avoid when checking solutions to linear systems of equations?

One common mistake is to incorrectly substitute values into the equations or to use the wrong signs for operations. It is also important to double check the arithmetic and algebraic steps taken to solve the system, as errors can easily occur.

4. Is there a specific order in which I should check the solution to a linear system of equations?

There is no specific order in which to check the solution, but it is recommended to start with the simplest equations and work your way up to the more complex ones. This can help to catch any errors early on.

5. Are there any shortcuts or tricks for quickly checking solutions to linear systems of equations?

There are no shortcuts or tricks for checking solutions to linear systems of equations by hand. It is important to carefully and accurately substitute values and verify that all equations are satisfied for each variable.

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