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

  • question_answer
    In order that the matrix \[\left[ \begin{matrix}    1 & 2 & 3  \\    4 & 5 & 6  \\    3 & \lambda  & 5  \\ \end{matrix} \right]\] be non-singular, \[\lambda \] should not be equal to  [Kurukshetra CEE 1998]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    Matrix \[\left[ \begin{matrix}    1 & 2 & 3  \\    4 & 5 & 6  \\    3 & \lambda  & 5  \\ \end{matrix} \right]\]be non singular, only if \[\left| \,\begin{matrix}    1 & 2 & 3  \\    4 & 5 & 6  \\    3 & \lambda  & 5  \\ \end{matrix}\, \right|\ne 0\] Þ \[\,1(25-6\lambda )-2(20-18)+3(4\lambda -15)\ne 0\] Þ  \[25-6\lambda -4+12\lambda -45\ne 0\] Þ \[6\lambda -24\ne 0\]Þ \[\lambda \ne 4\].


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