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

  • question_answer
    If \[A=\left[ \begin{matrix}    4 & 2  \\    3 & 4  \\ \end{matrix} \right]\],then \[|adj\,\,A|\]is equal to [UPSEAT 2003]

    A) 16

    B) 10

    C) 6

    D) None of these

    Correct Answer: B

    Solution :

           \[abc\,\left( 1+\sum \frac{1}{a} \right)\,\left| \,\begin{matrix}    1 & \frac{1}{b} & \frac{1}{c}  \\    0 & 1 & 0  \\    0 & 0 & 1  \\ \end{matrix}\, \right|\]  adj \[A=\left[ \begin{matrix}    4 & -2  \\    -3 & 4  \\ \end{matrix} \right]\] \[|adj\,A|\,=(4\times 4)-(-3\times -2)=16-6\] \[|adj\,A|\,\,=10.\]


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