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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
    \[\Delta =\left| \,\begin{matrix}    a & a+b & a+b+c  \\    3a & 4a+3b & 5a+4b+3c  \\    6a & 9a+6b & 11a+9b+6c  \\ \end{matrix}\, \right|\] where \[a=i,b=\omega ,c={{\omega }^{2}}\], then \[\Delta \]is equal to

    A) i

    B) \[-{{\omega }^{2}}\]

    C) \[\omega \]

    D) \[-i\]

    Correct Answer: A

    Solution :

    We first operating \[{{R}_{3}}-2{{R}_{2}}\] and \[{{R}_{2}}-3{{R}_{1}}\] in given determinant, then we get \[=a[{{a}^{2}}+ab-2{{a}^{2}}-ab]=-{{a}^{3}}=i\].


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