Can we say that a system in REF has no solution if the last column of the augmented matrix contains a leading entry. I am a little confused about REF and RREF. Do we need to use RREF to tell whether the system has a solution? OR just REF is enough to tell whether the system has no solutions, infinitely many solutions or one unique solution.
2026-03-27 16:53:17.1774630397
Differences between REF and RREF
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REF is enough. RREF will give you the solutions if any, but REF is enough since the necessary and sufficient condition to have no solution is that the rank of the augmented matrix is greater than the rank of the matrix of the linear system.