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

  • question_answer
    If \[A=\left| \,\begin{matrix}    5 & 6 & 3  \\    -4 & 3 & 2  \\    -4 & -7 & 3  \\ \end{matrix}\, \right|\,,\]then cofactors of the elements of 2nd row are [RPET 2002]

    A) \[39,\,-3,\,11\]

    B) \[-39,\,3,\,11\]

    C) \[-39,\,27,\,11\]

    D) \[-39,\,-3,\,11\]

    Correct Answer: C

    Solution :

    \[{{C}_{21}}={{(-1)}^{2+1}}(18+21)=-39\] \[{{C}_{22}}={{(-1)}^{2+2}}(15+12)=27\] \[{{C}_{23}}={{(-1)}^{2+3}}(-35+24)=11\].


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