Re: Linear Algebra help Matrix

Quote:

Originally Posted by

**ILikeSerena** This is what you already had:

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

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?

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?

Re: Linear Algebra help Matrix

Quote:

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?

Re: Linear Algebra help Matrix

Quote:

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

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?

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?

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.

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

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?

Re: Linear Algebra help Matrix

Quote:

Originally Posted by

**ILikeSerena** Is this allowed?

Is this possible?

no, so does s = 3?

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?