The system of linear equations x + y + z = 2 2 x + 3 y + 2 z = 5 2 x + 3 y + a 2 - 1 z = a + 1

Step-by-step solution

Here, D = 1 1 1 2 3 2 2 3 a 2 - 1 = a 2 - 3 Hence at | a | = 3 , D = 0 . So system don't have unique solution. At a = 4 , D ≠ 0 , So, system has unique solution. Hence not inconsistent. At | a | = 3 , D = 0 and 2 n d & 3 r d equation are parallel. Hence no solution are possible. Hence, system is inconsistent for | a | = 3