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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
    \[\Delta =\left| \,\begin{matrix}    a+x & b & c  \\    b & x+c & a  \\    c & a & x+b  \\ \end{matrix}\, \right|\],which of the following is a factor for the above determinant         [Tamilnadu (Engg.) 2002]

    A) \[x-(a+b+c)\]

    B) \[x+(a+b+c)\]

    C) \[a+b+c\]

    D) \[-(a+b+c)\]

    Correct Answer: B

    Solution :

    Operating \[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}}\] we find that \[x+a+b+c\] is a factor.


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