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J & K CET Engineering J and K - CET Engineering Solved Paper-2006

  • question_answer
    The value of \[\lambda \] such that \[x+3y+\lambda z=0,\]\[2x+4y-z=0,\,\,\,\,\,\,\,x+5y-2z=0\]has a non-trivial solution is                    

    A)  \[-1\]             

    B)  \[0\]

    C)  \[1\]             

    D)  \[2\]

    Correct Answer: A

    Solution :

    Since, given equations have a non-trivial solution \[\therefore \] \[\Delta =0\] \[\Rightarrow \] \[\left| \begin{matrix}    1 & 3 & \lambda   \\    2 & 4 & -1  \\    1 & 5 & -2  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[1(-8+5)-3(-4+1)+\lambda (10-4)=0\] \[\Rightarrow \] \[-3+9+6\lambda =0\] \[\Rightarrow \] \[6\lambda =-6\] \[\Rightarrow \] \[\lambda =-1\]


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