2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Determinants & Matrices

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

  • question_answer
    If \[A=\left[ \begin{matrix}    -1 & 2  \\    2 & -1  \\ \end{matrix} \right]\]and \[B=\left[ \begin{align}   & 3 \\  & 1 \\ \end{align} \right],AX=B\], then \[X=\] [MP PET 2002]

    A) [5 7]

    B) \[\frac{1}{3}\left[ \begin{align}   & 5 \\  & 7 \\ \end{align} \right]\]

    C) \[\frac{1}{3}[5\,\,7]\]

    D) \[\left[ \begin{align}   & 5 \\  & 7 \\ \end{align} \right]\]

    Correct Answer: B

    Solution :

    \[A=\left[ \,\begin{matrix}    -1 & 2  \\    2 & -1  \\ \end{matrix}\, \right]\,\,,\,\,\,B=\left[ \begin{align}   & 3 \\  & 1 \\ \end{align} \right]\] \[AX=B\,\Rightarrow X={{A}^{-1}}B\] \[{{A}^{-1}}=\frac{adj\,A}{|A|}\] \[{{A}^{-1}}=\frac{-1}{3}\left[ \,\begin{matrix}    -1 & -2  \\    -2 & -1  \\ \end{matrix}\, \right]\]\[=\frac{1}{3}\left[ \,\begin{matrix}    1 & 2  \\    2 & 1  \\ \end{matrix}\, \right]\] and \[X={{A}^{-1}}B\] = \[\left[ \,\begin{matrix}    \frac{1}{3} & \frac{2}{3}  \\    \frac{2}{3} & \frac{1}{3}  \\ \end{matrix}\, \right]\,\left[ \begin{align}   & 3 \\  & 1 \\ \end{align} \right]\]; \[X=\frac{1}{3}\left[ \begin{align}   & 5 \\  & 7 \\ \end{align} \right]\].


You need to login to perform this action.
You will be redirected in 3 sec spinner