2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Solved Paper-2015

  • question_answer
    If \[A=\left[ \begin{matrix}    1 & 2 & 2  \\    2 & 1 & -2  \\    a & 2 & b  \\ \end{matrix} \right]\]is a matrix satisfying the equation \[A{{A}^{T}}=9I,\] where I is \[3\times 3\] identity matrix, then the ordered pair (a,b) is equal to : [JEE Main Solved Paper-2015 ]

    A) (2,1)                                      

    B) -(-2,-1)

    C) (2,-1)                    

    D) (-2,1)

    Correct Answer: B

    Solution :

    \[A{{A}^{T}}=9I\]\[\left[ \begin{matrix}    9 & 0 & a+4+2b  \\    0 & a & 2a+2-2b  \\    a+4+2b & 2a+2-2b & {{a}^{2}}+4+{{b}^{2}}  \\ \end{matrix} \right]=\left[ \begin{matrix}    9 & 0 & 0  \\    0 & 0 & 9  \\    0 & 0 & 9  \\ \end{matrix} \right]\] \[\Rightarrow \]\[\left\{ \begin{align}   & a+4+2b=0 \\  & 2a+2-2b=9 \\ \end{align} \right.\Rightarrow (a,b)=(-2,-1)\]44RA


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