No Solution to 3 Linear Equations Using Cramer's Rule

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SUMMARY

When solving three linear equations in three variables using Cramer's Rule, if the determinant of the coefficient matrix (det(A)) is zero, it indicates that the equations are linearly dependent. This results in an infinite number of solutions rather than a unique solution. The condition Ax = b confirms that the system does not have a unique solution when det(A) = 0, leading to the conclusion that the equations are not independent.

PREREQUISITES
  • Cramer's Rule for solving linear equations
  • Understanding of determinants in linear algebra
  • Concept of linear dependence and independence
  • Basic knowledge of matrix operations
NEXT STEPS
  • Study the implications of linear dependence in systems of equations
  • Learn about alternative methods for solving linear equations, such as Gaussian elimination
  • Explore the properties of determinants in greater detail
  • Investigate the geometric interpretation of linear equations and their solutions
USEFUL FOR

Students of linear algebra, mathematicians, and anyone involved in solving systems of linear equations using Cramer's Rule.

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while solving 3 linear equations in 3 variables by cramer's rule if all the determinant's are 0 then what can we conclude?
 
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if Ax=b
det(A)=0
we get 3 linearly dependent equations, hence you can construct infinite solutions to the equations.
 

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