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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