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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
    The determinant \[\left| \,\begin{matrix}    a & b & a-b  \\    b & c & b-c  \\    2 & 1 & 0  \\ \end{matrix}\, \right|\] is equal to zero if \[a,b,c\]are in [UPSEAT 2002]

    A) G. P.

    B) A. P.

    C) H. P.

    D) None of these

    Correct Answer: A

    Solution :

    On expanding, \[-a(b-c)+2b(b-c)+(a-b)(b-2c)=0\] Þ \[-ab+ac+2{{b}^{2}}-2bc+ab-2ac-{{b}^{2}}+2bc=0\] Þ \[{{b}^{2}}-ac=0\]   Þ  \[{{b}^{2}}=ac\].


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