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

  • question_answer
    If the system of equations \[x-ky-z=0\], \[kx-y-z=0\] and \[x+y-z=0\] has a non zero solution, then the possible value of k are [IIT Screening 2000]

    A) - 1, 2

    B) 1, 2

    C) 0, 1

    D) - 1, 1

    Correct Answer: D

    Solution :

    For non-trivial solution \[\Delta =0\] Þ \[\left| \,\begin{matrix}    1 & -k & -1  \\    k & -1 & -1  \\    1 & 1 & -1  \\ \end{matrix}\, \right|\,=\,0\]  Þ \[k=1,\,-1.\]


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