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

  • question_answer
    If \[A=\left[ \begin{matrix}    0 & 2  \\    3 & -4  \\ \end{matrix} \right]\] and  \[kA=\left[ \begin{matrix}    0 & 3a  \\    2b & 24  \\ \end{matrix} \right]\], then the values of k, a, b are respectively [EAMCET 2001]

    A) \[-\,6,-\,12,-\,18\]

    B) - 6, 4, 9

    C) \[-\,6,-\,4,-\,9\]

    D) - 6, 12, 18

    Correct Answer: C

    Solution :

    Given, \[kA=\left[ \,\begin{matrix}    0 & 3a  \\    2b & 24  \\ \end{matrix}\, \right]\]Þ \[k\,\,\left[ \begin{matrix}    0 & 2  \\    3 & -4  \\ \end{matrix} \right]\,=\,\left[ \begin{matrix}    0 & 3a  \\    2b & 24  \\ \end{matrix} \right]\] Þ \[2k=3a,\,3k=2b,\,-4k=24\] Þ  \[a=\frac{2k}{3},\,\,\,b=\frac{3k}{2},\,k=-6\] \[\Rightarrow \] \[k=-6,\,\,a=-4,\,b=-9\].


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