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
    \[\left| \,\begin{matrix}    1/a & 1 & bc  \\    1/b & 1 & ca  \\    1/c & 1 & ab  \\ \end{matrix}\, \right|=\] [RPET 2002]

    A) 0

    B) abc

    C) 1/abc

    D) None of these

    Correct Answer: A

    Solution :

    \[\Delta =\frac{1}{a}[ab-ca]+1\left[ ca.\frac{1}{c}-\frac{1}{b}.ab \right]+bc\left[ \frac{1}{b}-\frac{1}{c} \right]\] Þ\[\Delta =(b-c)+1(a-a)+(c-b)\]Þ \[\Delta =0\].


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