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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    If \[\left[ \begin{matrix}    2+x & 3 & 4  \\    1 & -1 & 2  \\    x & 1 & -5  \\ \end{matrix} \right]\]is a singular matrix, then x is  [Kerala (Engg.) 2001]

    A) \[\frac{13}{25}\]

    B) \[-\frac{25}{13}\]

    C) \[\frac{5}{13}\]

    D) \[\frac{25}{13}\]

    Correct Answer: B

    Solution :

    Given, \[\left| \,\begin{matrix}    2+x & 3 & 4  \\    1 & -1 & 2  \\    x & 1 & -5  \\ \end{matrix}\, \right|\,=0\] Þ  \[(2+x)(5-2)-3(-5-2x)+4(1+x)=0\] Þ  \[6+3x+15+6x+4+4x=0\] Þ  \[13x=-25\Rightarrow x=-\frac{25}{13}\].


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