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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 value of \[\lambda \] for which the system of equations \[2x-y-z=12,\]\[x-2y+z=-4,\]\[x+y+\lambda z=4\] has no solution is [IIT Screening 2004]

    A) 3

    B) - 3

    C) 2

    D) - 2

    Correct Answer: D

    Solution :

    The coefficient determinant \[D=\left| \,\begin{matrix}    2 & -1 & -1  \\    1 & -2 & 1  \\    1 & 1 & \lambda   \\ \end{matrix}\, \right|\]        = \[3\lambda -6\] For no solution, the necessary condition is \[D=0\] i.e., \[-3\lambda -6=0\Rightarrow \lambda =-2\] It can be seen that for \[\lambda =-2,\] there is no solution for the given system or equations.


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