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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 \[\left| \,\begin{matrix}    a & b & c  \\    m & n & p  \\    x & y & z  \\ \end{matrix}\, \right|=k\], then \[\left| \,\begin{matrix}    6a & 2b & 2c  \\    3m & n & p  \\    3x & y & z  \\ \end{matrix}\, \right|=\] [Tamilnadu (Engg.) 2002]

    A) \[k/6\]

    B) \[2k\]

    C) \[3k\]

    D) \[6k\]

    Correct Answer: D

    Solution :

    \[\left| \,\begin{matrix}    6a & 2b & 2c  \\    3m & n & p  \\    3x & y & z  \\ \end{matrix}\, \right|\] = 2 × 3 \[\left| \,\begin{matrix}    a & b & c  \\    m & n & p  \\    x & y & z  \\ \end{matrix}\, \right|=6k\].


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