JEE Main & Advanced Mathematics Matrices Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix

Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix

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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