# Thread: Linear Algebra help Matrix

1. ## Re: Linear Algebra help Matrix

Originally Posted by ILikeSerena

You can rewrite it into inequalities for t as follows.

$\displaystyle t \le 2+s$

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

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

$\displaystyle t \ge 0$

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

2. ## Re: Linear Algebra help Matrix

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?
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?

3. ## Re: Linear Algebra help Matrix

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

I really am not getting it, and i dont know how any of this makes t = 0. and makes s have only one value?

4. ## Re: Linear Algebra help Matrix

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

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

Suppose s=1, will this hold (what do you get)?
Or for s=2?
For which $\displaystyle s \ge 0$ will it hold?

5. ## Re: Linear Algebra help Matrix

Originally Posted by ILikeSerena
Slight modification:

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

Suppose s=1, will this hold (what do you get)?
Or for s=2?
For which $\displaystyle s \ge 0$ will it hold?
I get 3/9<t<3/19 so it doesnt hold

6. ## Re: Linear Algebra help Matrix

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?

7. ## Re: Linear Algebra help Matrix

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?

8. ## Re: Linear Algebra help Matrix

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.

9. ## Re: Linear Algebra help Matrix

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

10. ## Re: Linear Algebra help Matrix

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

s = 2
10/9<t<10/19
Is this possible?

11. ## Re: Linear Algebra help Matrix

Originally Posted by ILikeSerena
Is this allowed?

Is this possible?
no, so does s = 3?

12. ## Re: Linear Algebra help Matrix

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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