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J & K CET Engineering J and K - CET Engineering Solved Paper-2009

  • question_answer
    If the system of homogeneous equations \[2x-y+z=0,\,\,x-2y+z=0,\,\,\lambda \,\,x-y+2z=0\] has infinitely many solutions, then

    A)  \[\lambda =5\]         

    B)  \[\lambda =-5\]

    C)  \[\lambda \ne \pm 5\]        

    D)  None of these

    Correct Answer: A

    Solution :

    If given system of equations have infinitely many solutions, then \[\left| \begin{matrix}    2 & -1 & 1  \\    1 & -2 & 1  \\    \lambda  & -1 & 2  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(-4+1)+1(2-\lambda )+1(-1+2\lambda )=0\] \[\Rightarrow \] \[-6+2-\lambda -1+2\lambda =0\] \[\Rightarrow \] \[\lambda -5=0\] \[\Rightarrow \] \[\lambda =5\]


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