Results 1 to 2 of 2

Thread: Inequality

  1. #1
    Senior Member
    Joined
    Apr 2009
    Posts
    310

    Inequality



    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?

    cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    1. Independently of $\displaystyle a,b$ we have $\displaystyle a_{11},a_{12},a_{13}$ non negative.

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

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

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

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

    So, the solution is the region $\displaystyle R$ of the $\displaystyle ab$ plane:

    $\displaystyle R \equiv\begin{Bmatrix}2a+b\geq 0\\a\geq -1/8\\0\leq b<1/4\end{matrix}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jan 11th 2011, 08:20 PM
  2. Replies: 3
    Last Post: Dec 12th 2010, 01:16 PM
  3. inequality
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jul 26th 2010, 04:34 AM
  4. inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Jul 24th 2010, 12:08 PM
  5. Inequality
    Posted in the Algebra Forum
    Replies: 0
    Last Post: Oct 8th 2009, 03:06 AM

Search Tags


/mathhelpforum @mathhelpforum