Cramer's Rule: A Simplified Explanation

In summary, Cramer's Rule is a method used in linear algebra to solve systems of linear equations by using determinants and ratios. It is typically used when there are an equal number of equations and variables in a system and is more efficient for smaller systems. However, it has limitations as it can only be used for linear equations and becomes more computationally intensive for larger systems.
  • #1
rock.freak667
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Is there any simpler proof for Cramer's rule because I've been trying to understand it from this site and some of it I just don't get

http://planetmath.org/encyclopedia/ProofOfCramersRule.html
 
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  • #2
http://www.math.psu.edu/levi/231H/cramer.pdf
 
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  • #3
Well thanks, that kind of helps me a little
 

1. What is Cramer's Rule?

Cramer's Rule is a method used in linear algebra to solve systems of linear equations. It involves using determinants to find the unique solution or solutions to a system of equations.

2. How does Cramer's Rule work?

Cramer's Rule involves calculating the determinants of matrices and using them to find the values of the variables in a system of equations. The determinants are then used to form ratios that can be used to solve for the variables.

3. When is Cramer's Rule used?

Cramer's Rule is typically used when there are an equal number of equations and variables in a system of linear equations. It is also useful when dealing with small systems of equations, as it can be more efficient than other methods of solving.

4. What are the limitations of Cramer's Rule?

Cramer's Rule can only be used to solve systems of equations with an equal number of equations and variables. It also becomes more computationally intensive as the size of the system increases, making it less practical for larger systems of equations.

5. Can Cramer's Rule be used for non-linear equations?

No, Cramer's Rule can only be used for systems of linear equations. Non-linear equations cannot be solved using determinants and ratios, which are the key components of Cramer's Rule.

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