Consistency of a System of Linear Equation
Category : JEE Main & Advanced
In system of linear equations \[AX=B,\,A={{({{a}_{ij}})}_{n\times n}}\] is said to be
(i) Consistent (with unique solution) if \[|A|\ne 0\].
i.e., if \[A\] is non-singular matrix.
(ii) Inconsistent (It has no solution) if \[|A|=0\] and \[(adjA)\,B\] is a non-null matrix.
(iii) Consistent (with infinitely \[m\] any solutions) if \[|A|\,=\,0\] and \[(adj\,A)\,B\] is a null matrix.
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