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JCECE Engineering JCECE Engineering Solved Paper-2013

  • question_answer
    Matrix \[{{M}_{r}}\] is defined as\[{{M}_{r}}=\left[ \begin{matrix}    r & r-1  \\    r-1 & r  \\ \end{matrix} \right]\],\[r\in N\]value of\[\det ({{M}_{1}})+\det ({{M}_{2}})+\det ({{M}_{3}})\]\[+...+\det ({{M}_{2007}})\]is

    A) \[2007\]                              

    B) \[2008\]

    C) \[{{(2008)}^{2}}\]                            

    D) \[{{(2007)}^{2}}\]

    Correct Answer: B

    Solution :

    \[\det ({{M}_{r}})=\left| \begin{matrix}    r & r-1  \\    r-1 & r  \\ \end{matrix} \right|=2r-1\]                 \[\sum\limits_{r=1}^{2007}{\det }({{M}_{r}})2\sum\limits_{r=1}^{2007}{(r-2007)}\]                                 \[=2\times \frac{2007\times 2008}{2}-2007\]                 \[={{(2007)}^{2}}\]


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