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Math Help - Linear Algebra help Matrix

  1. #16
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by ILikeSerena View Post
    This is what you already had:




    You can rewrite it into inequalities for t as follows.

      t \le 2+s

     t \le (-4 + 7s) / 19

     t \ge (-4+7s) / 9

     t \ge 0

    Do you notice anything strange about the 2nd and 3rd inequality?

    They dont hold, cause t is has to be greater than or equal to zero, but less than or equal to 2+s
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  2. #17
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
    They dont hold, cause t is has to be greater than or equal to zero, but less than or equal to 2+s
    Huh? They don't hold?
    These inequalities follow straight from your problem statement - they have to hold!
    The only question is, what restrictions do they place on s and t exactly?

    Yes, t has to be greater than or equal to zero and less than or equal to 2+s.
    But the 2nd and 3rd inequality place further restrictions on t... but which restrictions?
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  3. #18
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    Re: Linear Algebra help Matrix

     (-4+7s) / 9  \ge   t  \le (-4 + 7s) / 19 ?

    I really am not getting it, and i dont know how any of this makes t = 0. and makes s have only one value?
    Last edited by Tweety; February 20th 2013 at 12:48 PM.
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  4. #19
    Super Member ILikeSerena's Avatar
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
     (-4+7s) / 9  \ge   t  \le (-4 + 7s) / 19 ?
    Slight modification:

     (-4+7s) / 9  \le   t  \le (-4 + 7s) / 19

    Suppose s=1, will this hold (what do you get)?
    Or for s=2?
    For which s \ge 0 will it hold?
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  5. #20
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by ILikeSerena View Post
    Slight modification:

     (-4+7s) / 9  \le   t  \le (-4 + 7s) / 19

    Suppose s=1, will this hold (what do you get)?
    Or for s=2?
    For which s \ge 0 will it hold?
    I get 3/9<t<3/19 so it doesnt hold
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  6. #21
    Super Member ILikeSerena's Avatar
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
    I get 3/9<t<3/19 so it doesnt hold
    Nope. It does not hold for s=1.
    How about for other values of s?
    Perhaps s=0?
    Or a value of s such that -4+7s=0?
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  7. #22
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by ILikeSerena View Post
    Nope. It does not hold for s=1.
    How about for other values of s?
    Perhaps s=0?
    Or a value of s such that -4+7s=0?
    s = 4/7, but how does this prove that t = o and s has only one value?
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  8. #23
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
    s = 4/7, but how does this prove that t = o and s has only one value?
    Well, you didn't say what you get if s=2, or s=0...
    Which inequalities do you get in those cases?

    Alternatively can you make a graph with:
    - s on the horizontal axis
    - t on the vertical axis
    - the line l given by t=(-4 + 7s)/9
    - the line m given by t=(-4 + 7s)/19
    We would be looking for values of t that are above line l and below line m.
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  9. #24
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by ILikeSerena View Post
    Well, you didn't say what you get if s=2, or s=0...
    Which inequalities do you get in those cases?

    Alternatively can you make a graph with:
    - s on the horizontal axis
    - t on the vertical axis
    - the line l given by t=(-4 + 7s)/9
    - the line m given by t=(-4 + 7s)/19
    We would be looking for values of t that are above line l and below line m.
    when s = 0
    -4/9<t<-4/19

    s = 2
    10/9<t<10/19
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  10. #25
    Super Member ILikeSerena's Avatar
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
    when s = 0
    -4/9<t<-4/19
    Is this allowed?

    s = 2
    10/9<t<10/19
    Is this possible?
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  11. #26
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by ILikeSerena View Post
    Is this allowed?



    Is this possible?
    no, so does s = 3?
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  12. #27
    Super Member ILikeSerena's Avatar
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    Re: Linear Algebra help Matrix

    Quote Originally Posted by Tweety View Post
    no, so does s = 3?
    Why is s=-1 not allowed exactly?
    Why is s=0 not allowed exactly?
    Why is s=1 not allowed exactly?
    Why is s=2 not allowed exactly?

    And ultimately, why is s = 4/7 allowed?
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