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
    \[\left| \,\begin{matrix}    5 & 3 & -1  \\    -7 & x & -3  \\    9 & 6 & -2  \\ \end{matrix}\, \right|=0\], then x is equal to [Pb. CET 2002]

    A) 3

    B) 5

    C) 7

    D) 9

    Correct Answer: D

    Solution :

    We have \[\Delta =\left| \,\begin{matrix}    5 & 3 & -1  \\    -7 & x & -3  \\    9 & 6 & -2  \\ \end{matrix}\, \right|\text{ }=\text{0}\] \[\therefore \] \[-10x+90-42-81+42+9x=0\,\,\text{or}\,\text{ }x=9\].


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