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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
    \[\left| \,\begin{matrix}    a+b & b+c & c+a  \\    b+c & c+a & a+b  \\    c+a & a+b & b+c  \\ \end{matrix}\, \right|=K\,\,\left| \,\begin{matrix}    a & b & c  \\    b & c & a  \\    c & a & b  \\ \end{matrix}\, \right|\,,\]then \[K=\] [EAMCET 1992; DCE 2000]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: B

    Solution :

    The determinant can be written sum of \[2\times 2\times 2=8\] determinants of which 6 are reduces to zero because of their two rows are identical. Hence proceed.


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