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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Special types of matrices, Transpose, Adjoint and Inverse of matrices

  • question_answer
    The matrix \[\left( \begin{matrix}    1 & a & 2  \\    1 & 2 & 5  \\    2 & 1 & 1  \\ \end{matrix} \right)\]is not invertible, if ?a? has the value [MP PET 1998]

    A) 2

    B) 1

    C) 0

    D) -1

    Correct Answer: B

    Solution :

    The matrix is not invertible if \[\left| \,\begin{matrix}    1 & a & 2  \\    1 & 2 & 5  \\    2 & 1 & 1  \\ \end{matrix}\, \right|=0\] \[\Rightarrow \] \[1\,(2-5)-a(1-10)+2(1-4)=0\] \[\Rightarrow \] \[-3+9a-6=0\Rightarrow a=1\].


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