The system of equations alpha x plus y plus z equals alpha minus 1 x plus alpha y plus z equals alpha minus 1 x plus y plus alpha z equals alpha minus 1has no solution, if alpha is

  1. Not – 2    
  2. 1    
  3. – 2    
  4. Either – 2 or 1    

The correct answer is: – 2

    For no solution or infinitely many solutions open vertical bar table row alpha 1 1 row 1 alpha 1 row 1 1 alpha end table close vertical bar equals 0 rightwards double arrow alpha equals 1 comma alpha equals negative 2.
    But for alpha equals 1, clearly there are infinitely many solutions and when we put alpha equals negative 2 in given system of equations and adding them together L.H.S not equal to R.H.S. i.e., No solution.

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