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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 \[A=\left| \,\begin{matrix}    -1 & 2 & 4  \\    3 & 1 & 0  \\    -2 & 4 & 2  \\ \end{matrix}\, \right|\]and \[B=\left| \,\begin{matrix}    -2 & 4 & 2  \\    6 & 2 & 0  \\    -2 & 4 & 8  \\ \end{matrix}\, \right|\], then B is given by [Tamilnadu (Engg.) 2002]

    A) \[B=4A\]

    B) \[B=-4A\]

    C) \[B=-A\]

    D) \[B=6A\]

    Correct Answer: B

    Solution :

    B is obtained from A by the operations \[{{R}_{1}}\leftrightarrow {{R}_{3}},\,\,{{R}_{3}}\to 2{{R}_{3}}\] and \[({{\sin }^{2}}{{60}^{o}}+{{\sin }^{2}}{{60}^{o}}+{{\sin }^{2}}{{60}^{o}})\]. Hence, \[B=(-1)\,4A=-4A\].


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