# solution to system of equations

by ashwani yadav   Last Updated August 10, 2018 05:20 AM

In a system of equations AX = B. by Cramer's rule if det(A)=0, then the system will have no solution but on the other hand, in non-homogeneous system of equations suppose the rank of square matrix nxn is (n-1) and rank of the augmented matrix[A|B] is also having the same rank but then we say that system is consistent, having rank < no. of variables implies infinitely many solutions.

how is this correct? I mean if the rank of A is n-1 < n and rank(A) = rank(A|B), then it also implies that determinant of square matrix nxn is zero but then we say it is consistent.

pls correct me if my theory is wrong too.

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