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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 element in the first row and third column of the inverse of the matrix \[\left[ \begin{matrix}    1 & 2 & -3  \\    0 & 1 & 2  \\    0 & 0 & 1  \\ \end{matrix} \right]\]is [MP PET 2000]

    A) - 2

    B) 0

    C) 1

    D) 7

    Correct Answer: D

    Solution :

    Let \[A=\left[ \,\begin{matrix}    1 & 2 & -3  \\    0 & 1 & 2  \\    0 & 0 & 1  \\ \end{matrix}\, \right]\] Þ |A| = 1 \[adj\,(A)={{\left[ \begin{matrix}    1 & 2\,\,\, & -1  \\    -2 & 1 & 1  \\    7\,\, & -2 & 1  \\ \end{matrix} \right]}^{T}}\]. Hence, \[{{A}^{-1}}=\frac{adj\,(A)}{|A|}\] Þ \[{{A}^{-1}}=\left[ \begin{matrix}    1 & -2 & 7  \\    2 & 1 & -2  \\    -1 & 1 & 1  \\ \end{matrix} \right]\] . Hence, element\[z=3\].


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