JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    The matrix \[\left[ \begin{matrix}    \lambda  & -1 & 4  \\    -3 & 0 & 1  \\    -1 & 1 & 2  \\ \end{matrix} \right]\]is invertible, if [Kurukshetra CEE 1996]

    A) \[\lambda \ne -15\]

    B) \[\lambda \ne -17\]

    C) \[\lambda \ne -16\]

    D) \[\lambda \ne -18\]

    Correct Answer: B

    Solution :

    \[\left| \,\begin{matrix}    \lambda  & -1 & 4  \\    -3 & 0 & 1  \\    -1 & 1 & 2  \\ \end{matrix}\, \right|\,\ne 0\Rightarrow \lambda \ne -17\].


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