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JEE Main & Advanced JEE Main Paper (Held On 12 April 2014)

  • question_answer
    If\[A=\left[ \begin{matrix}    1 & 2 & x  \\    3 & -1 & 2  \\ \end{matrix} \right]\]and\[B=\left[ \begin{align}   & y \\  & x \\  & 1 \\ \end{align} \right]\]be such that\[AB=\left[ \begin{align}   & 6 \\  & 8 \\ \end{align} \right],\]then:   [JEE Main Online Paper ( Held On 12 Apirl  2014 )

    A) \[y=2x\]                              

    B) \[y=2x\]

    C) \[y=x\]                

    D) \[y=-x\]

    Correct Answer: A

    Solution :

    Let\[A=\left[ \begin{matrix}    1 & 2 & x  \\    3 & -1 & 2  \\ \end{matrix} \right]\]and \[B=\left[ \begin{align}   & y \\  & x \\  & 1 \\ \end{align} \right]\] \[AB=\left[ \begin{matrix}    1 & 2 & x  \\    3 & -1 & 2  \\ \end{matrix} \right]\left[ \begin{align}   & y \\  & x \\  & 1 \\ \end{align} \right]\]\[\Rightarrow \left[ \begin{align}   & 6 \\  & 8 \\ \end{align} \right]=\left[ \begin{matrix}    \begin{align}   & y+2x+x \\  & 3y-x+2 \\ \end{align}  \\ \end{matrix} \right]\] \[\Rightarrow \]\[y+3x=6\]and \[3y-x=6\] On solving, we get\[x=\frac{6}{5}\]and \[y=\frac{12}{5}\]\[\Rightarrow \]\[y=2x\]


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