2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced AIEEE Solved Paper-2012

  • question_answer
    Let \[A=\left( \begin{matrix}   1 & 0 & 0  \\   2 & 1 & 0  \\    3 & 2 & 1  \\ \end{matrix} \right)\]. If \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] are column matrices such that \[A{{u}_{1}}\left( \begin{align}   & 1 \\  & 0 \\  & 0 \\ \end{align} \right)\] and \[A{{u}_{2}}\left( \begin{align}   & 0 \\  & 1 \\  & 0 \\ \end{align} \right)\], then \[{{u}_{1}}+{{u}_{2}}\] is equal to:   AIEEE  Solved  Paper-2012

    A) \[\left( \begin{align}   & -1 \\  & 1 \\  & 0 \\ \end{align} \right)\]                                          

    B) \[\left( \begin{align}   & -1 \\  & 1 \\  & -1 \\ \end{align} \right)\]

    C) \[\left( \begin{align}   & -1 \\  & -1 \\  & 0 \\ \end{align} \right)\]                                          

    D) \[\left( \begin{align}   & 1 \\  & -1 \\  & -1 \\ \end{align} \right)\]

    Correct Answer: D

    Solution :

                 \[A({{u}_{1}}+{{u}_{2}})=\left( \begin{align}   & 1 \\  & 1 \\  & 0 \\ \end{align} \right)\]                        \[\left| A \right|=1\] \[{{A}^{-1}}=\frac{1}{\left| A \right|}adj\,\,A\] \[{{u}_{1}}+{{u}_{2}}={{A}^{-1}}\left[ \begin{align}   & 1 \\  & 1 \\  & 0 \\ \end{align} \right]\]             \[{{A}^{-1}}=\left[ \begin{matrix}    1 & 0 & 0  \\    -2 & 1 & 0  \\    1 & -2 & 1  \\ \end{matrix} \right]=\left[ \begin{align}   & 1 \\  & -1 \\  & -1 \\ \end{align} \right]\]


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