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J & K CET Engineering J and K - CET Engineering Solved Paper-2007

  • question_answer
    The system of equations \[3x-y+4z=3\] \[x+2y-3z=-2\] \[6x+5y+\lambda z=-3\] has at least one solution, if

    A)  \[\lambda =-5\]       

    B)  \[\lambda =5\]

    C)  \[\lambda =3\]

    D)  \[\lambda =-13\]

    Correct Answer: A

    Solution :

    \[\therefore \]  \[\left| \begin{matrix}    3 & -1 & 4  \\    1 & 2 & -3  \\    6 & 5 & \lambda   \\ \end{matrix} \right|=0\] \[\Rightarrow \]  \[3(2\lambda +15)+1(\lambda +18)+4(5-12)=0\] \[\Rightarrow \] \[6\lambda +45+\lambda +18-28=0\] \[\Rightarrow \] \[7\lambda =-35\,\,\,\Rightarrow \,\,\,\,\lambda =-5\]


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