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Thread: Inequality

  1. #1
    Senior Member
    Apr 2009


    Hi, I was wondering what values of a and b such that the entries for this matrix are all non negative?

    What I did was:

    we know that 4b-1<0

    so we must have 4b=>0 and b+2a=>0 and 8a+1=>0

    then we get 0<=b<1/4 and a=>-1/8 and a=>b/-2

    we can find an interval for b but what about a?

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  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Nov 2010
    Madrid, Spain
    1. Independently of a,b we have a_{11},a_{12},a_{13} non negative.

    2. a_{22},a_{23},a_{33} are non negative iff 4b-1<0 i.e. b<1/4 .

    3. For b<1/4 , a_{32} is non negative iff b\geq 0 .

    4. For 0\leq b<1/4 , a_{21} is non negative iff 8a+1\geq 0 i.e. a\geq -1/8 .

    5. For 0\geq b<1/4 and a\geq -1/8 , a_{31} is non negative iff b+2a\geq 0 .

    So, the solution is the region R of the ab plane:

    R \equiv\begin{Bmatrix}2a+b\geq 0\\a\geq -1/8\\0\leq b<1/4\end{matrix}
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