# Linear Algebra help Matrix

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• Feb 20th 2013, 12:08 PM
Tweety
Re: Linear Algebra help Matrix
Quote:

Originally Posted by ILikeSerena

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
• Feb 20th 2013, 12:19 PM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
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? :confused:
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?
• Feb 20th 2013, 12:45 PM
Tweety
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?
• Feb 20th 2013, 12:48 PM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
$(-4+7s) / 9 \ge t \le (-4 + 7s) / 19$?

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?
• Feb 20th 2013, 12:50 PM
Tweety
Re: Linear Algebra help Matrix
Quote:

Originally Posted by ILikeSerena
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
• Feb 20th 2013, 12:52 PM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
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?
• Feb 21st 2013, 02:32 AM
Tweety
Re: Linear Algebra help Matrix
Quote:

Originally Posted by ILikeSerena
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?
• Feb 21st 2013, 04:17 AM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
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.
• Feb 21st 2013, 04:33 AM
Tweety
Re: Linear Algebra help Matrix
Quote:

Originally Posted by ILikeSerena
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
• Feb 21st 2013, 04:39 AM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
when s = 0
-4/9<t<-4/19

Is this allowed?

Quote:

s = 2
10/9<t<10/19
Is this possible?
• Feb 21st 2013, 04:42 AM
Tweety
Re: Linear Algebra help Matrix
Quote:

Originally Posted by ILikeSerena
Is this allowed?

Is this possible?

no, so does s = 3?
• Feb 21st 2013, 05:32 AM
ILikeSerena
Re: Linear Algebra help Matrix
Quote:

Originally Posted by Tweety
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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