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

  • question_answer
    The minors of - 4 and 9 and the co-factors of - 4 and 9 in determinant \[\,\left| \,\begin{matrix}    -1 & -2 & 3  \\    -4 & -5 & -6  \\    -7 & 8 & 9  \\ \end{matrix}\, \right|\] are respectively [J & K 2005]

    A) 42, 3; - 42, 3

    B) -42, -3; 42, -3

    C) 42, 3; - 42, - 3

    D) 42, 3; 42, 3

    Correct Answer: B

    Solution :

    Minor of - 4 = \[\left| \begin{matrix}    -2 & 3  \\    8 & 9  \\ \end{matrix}\, \right|=-42\], 9 = \[\left| \begin{matrix}    -1 & -2  \\    -4 & -5  \\ \end{matrix} \right|=-3\]and  cofactor of - 4 =\[{{(-1)}^{2+1}}(-42)=42\],cofactor of  9= \[{{(-1)}^{3+3}}(-3)=-3\] .


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