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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        If\[f(x)=\frac{1+x}{1-x}\]and A is matrix for which\[{{A}^{3}}=0,\]then f is equal to

    A)  \[I+A+{{A}^{2}}\]                           

    B)  \[I+2A+2{{A}^{2}}\]

    C)  \[I+A+{{A}^{2}}\]                           

    D)  None of these

    Correct Answer: B

    Solution :

                    \[\because \]\[(I-A)f(A)=I+A\] \[\Rightarrow \]\[f(A)=(I+A){{(I-A)}^{-1}}=(I+A)\] \[\therefore \]\[(I+A+{{A}^{2}})=I+A+{{A}^{2}}+A+{{A}^{2}}+{{A}^{3}}\]                 \[=I+2A+2{{A}^{2}}\]


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