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

  • question_answer
    If \[{{\Delta }_{1}}=\left| \,\begin{matrix}    1 & 0  \\    a & b  \\ \end{matrix}\, \right|\] and  \[{{\Delta }_{2}}=\left| \begin{matrix}    1 & 0  \\    c & d  \\ \end{matrix} \right|\], then \[{{\Delta }_{2}}{{\Delta }_{1}}\]is equal to [RPET 1984]

    A) ac

    B) bd

    C) \[(b-a)(d-c)\]

    D) None of these

    Correct Answer: B

    Solution :

    \[{{\Delta }_{2}}{{\Delta }_{1}}=\left| \begin{matrix}    1 & 0  \\    c & d  \\ \end{matrix} \right|\,\,\left| \,\begin{matrix}    1 & 0  \\    a & b  \\ \end{matrix}\, \right|=\left| \,\begin{matrix}    1 & 0  \\    c+ad & bd  \\ \end{matrix}\, \right|=bd\].


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