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JEE Main & Advanced AIEEE Solved Paper-2011

  • question_answer
    The number of values of k for which the linear equations \[4x+ky+2z=0\] \[kx+4y+z=0\] \[\left. 2x+2y+z=0 \right|\] possess a non-zero solution is.   AIEEE  Solved  Paper-2011

    A) Zero                                         

    B) 3

    C) 2                                                

    D) 1

    Correct Answer: C

    Solution :

                 For non-trivial solution of given system of linear equations \[\left| \begin{matrix}    4 & k & 2  \\    k & 4 & 1  \\    2 & 2 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow 8+k(2-k)+2(2k-8)=0\] \[\Rightarrow -{{k}^{2}}+6k-8=0\] \[\Rightarrow {{k}^{2}}-6k+8=0\] \[\Rightarrow k=2,4\] Clearly there exists two values of k.


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