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

  • question_answer
    If the matrix \[\left[ \begin{matrix}    1 & 3 & \lambda +2  \\    2 & 4 & 8  \\    3 & 5 & 10  \\ \end{matrix} \right]\]is singular, then \[\lambda =\]  [MP PET 1990; Pb. CET 2000]

    A) - 2

    B) 4

    C) 2

    D) - 4

    Correct Answer: B

    Solution :

    The matrix \[\left[ \begin{matrix}    1 & 3 & \lambda +2  \\    2 & 4 & 8  \\    3 & 5 & 10  \\ \end{matrix} \right]\] is singular, If \[\,\left| \,\begin{matrix}    1 & 3 & \lambda +2  \\    2 & 4 & 8  \\    3 & 5 & 10  \\ \end{matrix}\, \right|=0\] Þ \[1(40-40)-3(20-24)+(\lambda +2)(10-12)=0\] Þ \[2(\lambda +2)=12\Rightarrow \lambda =4.\]


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