JEE Main & Advanced Mathematics Determinants & Matrices Question Bank System of linear equations, Some special determinants, differentiation and integration of determinants

  • question_answer
    \[x+ky-z=0,3x-ky-z=0\]and \[x-3y+z=0\] has non-zero solution for k = [IIT 1988]

    A) - 1

    B) 0

    C) 1

    D) 2

    Correct Answer: C

    Solution :

    It has a non-zero solution if \[\left| \,\begin{matrix}    1 & \,\,k & -1  \\    3 & -k & -1  \\    1 & -3 & \,\,1  \\ \end{matrix} \right|\]=0 \[\Rightarrow -6k+6=0\Rightarrow k=1\].


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