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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
    If a system of the equation  \[{{(\alpha +1)}^{3}}x+{{(\alpha +2)}^{3}}y-{{(\alpha +3)}^{3}}=0\] and \[(\alpha +1)x+(\alpha +2)y-(\alpha +3)=0,x+y-1=0\]is constant. what is the value of \[\alpha \] [Orissa JEE 2005]

    A) 1

    B) 0

    C) - 3

    D) - 2

    Correct Answer: D

    Solution :

    For constant solution \[|A|=0\] i.e., \[\left| \,\begin{matrix}    {{(\alpha +1)}^{3}} & {{(\alpha +2)}^{3}} & -{{(\alpha +3)}^{3}}  \\    \alpha +1 & \alpha +2 & -(\alpha +3)  \\    1 & 1 & -1  \\ \end{matrix} \right|=0\] Þ \[6\alpha +12=0\Rightarrow \alpha =-2\].


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