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 \[\Delta =\left| \,\begin{matrix}    x & y & z  \\    p & q & r  \\    a & b & c  \\ \end{matrix}\, \right|,\]then \[\left| \,\begin{matrix}    x & 2y & z  \\    2p & 4q & 2r  \\    a & 2b & c  \\ \end{matrix}\, \right|\]equals [RPET 1999]

    A) \[{{\Delta }^{2}}\]

    B) \[4\Delta \]

    C) \[3\Delta \]

    D) None of these

    Correct Answer: B

    Solution :

    Let \[{{\Delta }_{1}}=\left| \,\begin{matrix}    x & 2y & z  \\    2p & 4q & 2r  \\    a & 2b & c  \\ \end{matrix}\, \right|\]=\[4\,\left| \,\begin{matrix}    x & y & z  \\    p & q & r  \\    a & b & c  \\ \end{matrix}\, \right|=4\Delta \]. (Taking common '2' from IInd row and '2' from IInd column).


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