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In a linear system of equations where there is a solution, is it possible for Cramer's rule to fail? By fail, as in end up with a zero determinate on either the top or the bottom or both.
uart said:Statdad, when the OP stated "In a linear system of equations where there is a solution" I took that to mean that there is a unique solution to the equations. In this case then all that I said above is true. Clearly Cramers rule will fail if there is not a unique solution.
Cramer's rule may fail if the matrix is singular or if the coefficients of the equations are not independent. This means that there may be no unique solution or an infinite number of solutions.
Yes, Cramer's rule can fail for any type of matrix. It is not limited to any specific type of matrix.
You can tell if Cramer's rule will fail by checking if the determinant of the matrix is equal to 0. If it is, then Cramer's rule will fail as there will be no unique solution.
Yes, Cramer's rule can fail even if the matrix is square. This can happen if the determinant of the matrix is equal to 0.
There are alternative methods to Cramer's rule, such as Gaussian elimination, that do not have the same limitations and potential for failure. However, the choice of method may depend on the specific problem at hand and the size and type of matrix being used.