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JEE Main & Advanced JEE Main Paper (Held On 15 April 2018) Slot-II

  • question_answer
    Suppose \[A\] is any \[3\times 3\] non-singular matrix and \[(A-3I)(A-5I)=O\], where \[I={{I}_{3}}\]  and \[O={{O}_{3}}\]. If \[\alpha A+\beta {{A}^{-1}}=4I\], then \[\alpha +\beta \] is equal to [JEE Online 15-04-2018 (II)]

    A) 8             

    B) 12          

    C) 13                          

    D)          7

    Correct Answer: A

    Solution :

                              We have \[(A-3I)(A-5I)=O\] \[{{A}^{2}}-8A+15I=O\] Multiplying both sides with \[{{A}^{-1}}\], we get \[A-8I+15{{A}^{-1}}=O\] \[A+15{{A}^{-1}}=8I\] \[\frac{A}{2}+\frac{15{{A}^{-1}}}{2}=4I\] \[\therefore \alpha +\beta =\frac{1}{2}+\frac{15}{2}=\frac{16}{2}=8\]


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