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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If the matrix \[\left[ \begin{matrix}    0 & 1 & -2  \\    -1 & 0 & 3  \\    \lambda  & -3 & 0  \\ \end{matrix} \right]\]is singular, then \[\lambda \]= [MP PET 1989]

    A) - 2

    B) - 1

    C) 1

    D) 2

    Correct Answer: D

    Solution :

    The matrix \[A=\left[ \begin{matrix}    \,\,0 & \,\,1 & -2  \\    -1 & \,\,0 & \,\,3  \\    \,\,\lambda  & -3 & \,\,0  \\ \end{matrix} \right]\] is singular Þ \[|A|\] = 0   Þ \[0-1(-3\lambda )+(-2)(3)=0\] \[\Rightarrow 3\lambda -6=0\Rightarrow \lambda =2\].


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