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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank System of linear equations, Some special determinants, differentiation and integration of determinants

  • question_answer
    The system of equations\[\begin{align}   & \alpha x+y+z=\alpha -1 \\  & x+\alpha y+z=\alpha -1 \\  & x+y+\alpha z=\alpha -1 \\ \end{align}\] has no solution, if \[\alpha \] is [AIEEE 2005]

    A) Not - 2

    B) 1

    C) - 2

    D) Either - 2 or 1

    Correct Answer: C

    Solution :

    For no solution or infinitely many solutions\[\left| \,\begin{matrix}    \alpha  & 1 & 1  \\    1 & \alpha  & 1  \\    1 & 1 & \alpha   \\ \end{matrix}\, \right|=0\Rightarrow \alpha =1,\alpha =-2\]. But for\[\alpha =1\], clearly there are infinitely many solutions and when we put \[\alpha =-2\] in given system of equations and adding them together L.H.S \[\ne \] R.H.S. i.e., No solution.


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