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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Minors and Co-factors, Product of determinants

  • question_answer
    The cofactor of the element '4' in the determinant \[\left| \,\begin{matrix}    1 & 3 & 5 & 1  \\    2 & 3 & 4 & 2  \\    8 & 0 & 1 & 1  \\    0 & 2 & 1 & 1  \\ \end{matrix}\, \right|\] is [MP PET 1987]

    A) 4

    B) 10

    C) - 10

    D) - 4

    Correct Answer: B

    Solution :

    The cofactor of element 4, in the 2nd row and \[{{3}^{rd}}\] column is \[={{(-1)}^{2+3}}\left| \begin{matrix}    1 & 3 & 1  \\    8 & 0 & 1  \\    0 & 2 & 1  \\ \end{matrix} \right|\]=- {1(- 2) - 3 (8 - 0)+ 1.16} = 10.


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