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Question

The system of equations,
axyz=α1,xayz=α1xyaz=α1
has no solution if α is 
  1. Either 2 or 1
  2. 2
  3. 1
  4. Not 2


Solution

The correct option is B 2
For no solution or infinitely many solutions.
∣ ∣α111α111α∣ ∣
or α(α21)1(α1)+1(1α)=0 
or α(α21)2α+2=0
or α(α1)(α+1)2(α1)=0
or (α1)(α2+α2)=0
or (α1)(α+2)(α1)=0
or (α1)2(α+2)=0
or α=1,2

But for α=1, there are infinite solutions.
When α=2, we have 
2xyz=3
x+2yz=3
xy+2z=3
Adding all equations, we get 0=9, which is not true.
Hence, there is no solution when α=2.

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