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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    If \[{{\left| \,\begin{matrix}    4 & 1  \\    2 & 1  \\ \end{matrix}\, \right|}^{2}}=\left| \,\begin{matrix}    3 & 2  \\    1 & x  \\ \end{matrix}\, \right|-\left| \,\begin{matrix}    x & 3  \\    -2 & 1  \\ \end{matrix}\, \right|\], then x = [RPET 1996]

    A) - 14

    B) 2

    C) 6

    D) 7

    Correct Answer: C

    Solution :

    \[\left| \,\begin{matrix}    4 & 1  \\    2 & 1  \\ \end{matrix}\, \right|\,\left| \,\begin{matrix}    4 & 1  \\    2 & 1  \\ \end{matrix}\, \right|=\left| \,\begin{matrix}    3 & 2  \\    1 & x  \\ \end{matrix}\, \right|-\left| \,\begin{matrix}    x & 3  \\    -2 & 1  \\ \end{matrix}\, \right|\]      \[=\left| \,\begin{matrix}    17 & 9  \\    9 & 5  \\ \end{matrix}\, \right|=(3x-2)-(x+6)\] Þ \[85-81=2x-8\] Þ \[4+8=2x\]Þ \[x=6\].


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