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The system of linear equations x + y + z = 2 , 2x + 3y + 2z = 5     ,  2x + 3y + (a2 – 1)z = a + 1

  • (1)  is inconsistent when a = 4
  • (2)  has infinitely many solutions for a = 4
  • (3)  has a unique solution for | a| = √3 
  • (4) is inconsistent when |a| = √3

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Correct option is inconsistent when |a|=3 

Solution::

D=|11123223a21| 

D=1(3a236)1(2a224)+1(66) 

D=3a292a2+6 

D=a23

|a|=3

inconsistent when |a|=3 

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