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 \[\Delta =\left| \,\begin{matrix}    a & b & c  \\    x & y & z  \\    p & q & r  \\ \end{matrix}\, \right|\], then \[\left| \,\begin{matrix}    ka & kb & kc  \\    kx & ky & kz  \\    kp & kq & kr  \\ \end{matrix}\, \right|\]= [RPET 1986]

    A) \[\Delta \]

    B) \[k\Delta \]

    C) \[3k\Delta \]

    D) \[{{k}^{3}}\Delta \]

    Correct Answer: D

    Solution :

    \[\left| \,\begin{matrix}    ka & kb & kc  \\    kx & ky & kz  \\    kp & kq & kr  \\ \end{matrix}\, \right|\,=\,{{k}^{3}}\,\left| \,\begin{matrix}    a & b & c  \\    x & y & z  \\    p & q & r  \\ \end{matrix}\, \right|={{k}^{3}}\Delta \].


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