for a system of linear equations we know that if (adjA )B = 0 THEN THE SYSTEM MAY OR** MAY NOT** BE CONSISTENT.Discuss when it will become consistent and when inconsistent. is it necessary that if consistent than infinitely many solutions will be occurring in the above case?

Consistent system-

A given system of equation is said to be consistent if it has one or more solutions.

Inconsistent system-

A given system of equation is said to be inconsistent if it has no solutions.

Case -1:

When |A| $\ne $0 , then the given system is consistent and it has a unique solution.

Case-2:

When |A|=0 and (adj A)B$\ne $0 , then the given system is inconsistent and it has a no solution.

Case -3:

When |A|=0 and (adj A)B=0 , then the given system is consistent and it has infinite solution.

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