No Solution to 3 Linear Equations Using Cramer's Rule

Thread starter phymatter
Start date Jan 31, 2011
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Cramer's rule Linear Linear equations

In summary, Cramer's Rule is a method used to solve systems of linear equations by finding the ratio of determinants. It can only be used for systems with the same number of equations as variables and involves finding determinants of matrices. Some limitations include computational intensity and the possibility of no unique solution. If there is no solution using Cramer's Rule, it means the system of equations is inconsistent.

Jan 31, 2011

phymatter

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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Jan 31, 2011

abhishek ghos

if Ax=b
det(A)=0
we get 3 linearly dependent equations, hence you can construct infinite solutions to the equations.

1. What is Cramer's Rule?

Cramer's Rule is a method used to solve systems of linear equations using determinants. It involves finding the ratio of two determinants to determine the values of the variables in the system.

2. Can Cramer's Rule be used to solve any system of linear equations?

No, Cramer's Rule can only be used to solve systems of linear equations with the same number of equations as variables. In other words, it can only be used for systems of equations with the same number of unknowns.

3. How does Cramer's Rule work?

Cramer's Rule involves finding the determinants of the coefficient matrix and the constant matrix. The values of the variables can then be determined by dividing the determinant of the constant matrix by the determinant of the coefficient matrix.

4. Are there any limitations to using Cramer's Rule?

Yes, there are some limitations to using Cramer's Rule. It can become computationally intensive for larger systems of equations and it may not always yield a unique solution. Additionally, if the determinant of the coefficient matrix is equal to 0, Cramer's Rule cannot be used.

5. What does it mean if there is no solution to 3 linear equations using Cramer's Rule?

If there is no solution to 3 linear equations using Cramer's Rule, it means that the system of equations is inconsistent and cannot be solved. This could occur if the equations are contradictory or if there are not enough equations to determine unique values for all variables.