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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 equation\[3x-2y+z=0\], \[\lambda x-14y+15z=0\], \[x+2y+3z=0\]have a non-trivial solution, then \[\lambda =\] [EAMCET 1993]

    A) 5

    B) - 5

    C) - 29

    D) 29

    Correct Answer: D

    Solution :

    If the given system of equations has a non-trivial solution, then \[\left| \,\begin{matrix}    3 & -2 & 1  \\    \lambda  & -14 & 15  \\    1 & 2 & 3  \\ \end{matrix}\, \right|=0\Rightarrow \lambda =29\].


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