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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 \[\left| \,\begin{matrix}    a & b & a+b  \\    b & c & b+c  \\    a+b & b+c & 0  \\ \end{matrix}\, \right|=0\]; then \[a,b,c\] are in   [AMU 2000]

    A) A. P.

    B) G. P.

    C) H. P.

    D) None of these

    Correct Answer: B

    Solution :

    Let a,b,c are in G.P. and assume \[{{A}_{13}}=-5\]  \[\therefore \,\,\,\,\,A=\left| \,\begin{matrix}    1 & 2 & 3  \\    2 & 4 & 6  \\    3 & 6 & 0  \\ \end{matrix}\, \right|\,\,=\,\,0\] .


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