Consider the system of equations ax+by+cz=2,bx+cy+az=2,cx+ay+bz=2where a,b,c are real numbers such that a+b+c=0then the system

Augmented matrix AD=abc2bca2cab2                                               R3→R1+R2+R2                                          ~abc2bca2a+b+ca+b+ca+b+c6                                           ~abc2bca20006 ∵a+b+c=0Here rankA=2 and rankAD=3∴rankA≠rankAD The given system is inconsistent