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

  • question_answer
    Adjoint of the matrix \[N=\left[ \begin{matrix}    -4 & -3 & -3  \\    1 & 0 & 1  \\    4 & 4 & 3  \\ \end{matrix} \right]\]is [MP PET 1989]

    A) N

    B) 2N

    C) - N

    D) None of these

    Correct Answer: A

    Solution :

    The cofactors of \[N=\left[ \begin{matrix}    -4 & -3 & -3  \\    1 & 0 & 1  \\    4 & 4 & 3  \\ \end{matrix} \right]\] are\[{{c}_{11}}=-4,\,{{c}_{12}}=1,\,{{c}_{13}}=4\];  \[{{c}_{21}}=-3,\,{{c}_{22}}=0,\,{{c}_{23}}=4\] \[{{c}_{31}}=-3,\,{{c}_{32}}=1,\,{{c}_{33}}=3\] \[\therefore \] \[adj\,N=\left[ \begin{matrix}    -4 & -3 & -3  \\    1 & 0 & 1  \\    4 & 4 & 3  \\ \end{matrix} \right]=N\].


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