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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
    The following system of equation\[3x-2y+z=0\], \[\lambda x-14y+15z=0\], \[x+2y-3z=0\]has a solution other than \[x=y=z=0\]for \[\lambda \] equal to [MP PET 1990]

    A) 1

    B) 2

    C) 3

    D) 5

    Correct Answer: D

    Solution :

    The system of equations has infinitely many (non-trivial) solution, if \[\Delta =0\] i.e., if \[\left| \,\begin{matrix}    3 & -2 & 1  \\    \lambda  & -14 & 15  \\    1 & 2 & -3  \\ \end{matrix}\, \right|=0\] Þ \[3(42-30)-\lambda (6-2)+1(-30+14)=0\]Þ \[\lambda =5\] .


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