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

The system of linear equations
x+y+z=2
2x+3y+2z=5
2x+3y+a2-1z=a+1
  1. is inconsistent when a=3
  2. has a unique solution for a=3
  3. has infinitely many solutions for a=4
  4. is inconsistent when a=4

Solution

Here, D=11123223a2-1

=a2-3

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 2nd & 3rd equation are parallel. Hence no solution are possible.

Hence, system is inconsistent for |a|=3

Asked in: JEE Main 2019 (09 Jan Shift 1)

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