Rank of a matrix:The rank of a matrix is the order of the largest square sub-matrix of whose determinant is different than zero.
A set of linear equations possesses a solution if and only if the rank of the augmented matrix is equal to the rank of the coefficient matrix.
Inconsistent system: The non homogeneous systems which have no solution or called inconsistent systems, otherwise they are called consistent systems.
Complete solution: If a non homogeneous system is consistent then its complete solution is the sum of the complete solution of the homogeneous system plus its particular solution for .
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