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Question

The value of lambda for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

  1. 3    
  2. -3    
  3. 2    
  4. -2    

The correct answer is: -2


    The question is as follows the value of lambda for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution, as we know for no solution case determinant of coefficients is equal to 0

    The given equations are
    2x-y-z=12
    x-2y+z=-4
    x+y+λz=4
    Their determinant =D
    For no solution case D=0
    open vertical bar table row 2 cell negative 1 end cell cell negative 1 end cell row 1 cell negative 2 end cell 1 row 1 1 lambda end table close vertical bar equals 0
    => 2(2λ1)+1(λ1)1(1+2)=0
    => 3λ6=0
    λ=2

    Hence λ=2 for no solution.

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