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 Post subject: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 18:26:20 UTC
 S.O.S. Oldtimer

Joined: Fri, 30 Oct 2009 16:33:10 UTC
Posts: 261
I was give x'=(A)x where A is a 2x2 matrix with R1=( 5/4 3/4) and R2= (3/4 5/4).

This is what I have managed so far:

I assumed x=Ee^(rt) so I have equation (B)(C)=(D) where B is R1=(5/4-r 3/4) and R2=(3/4 5/4-r); C is R1=(E1) and R2=(E2) and D is a 0 matrix.

Well I came up with r1= [5+2sqrt(77/20)]/4 and r2=[5-2sqrt(77/20)]/4

So my new equation is (F)(C)=(D) where E and D are the same matrices as before and F is R1=(5/4-r1 3/4) and R2=(3/4 5/4-r2).

Now I think I need to observe the relation between E1 and E2; however, I do not see the relation - one does not appear to be a multiple of the other to me. Did I make a mistake?

Thanks

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 Post subject: Re: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 18:41:18 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12071
Location: Austin, TX
goteamusa wrote:
I was give x'=(A)x where A is a 2x2 matrix with R1=( 5/4 3/4) and R2= (3/4 5/4).

This is what I have managed so far:

I assumed x=Ee^(rt) so I have equation (B)(C)=(D) where B is R1=(5/4-r 3/4) and R2=(3/4 5/4-r); C is R1=(E1) and R2=(E2) and D is a 0 matrix.

Well I came up with r1= [5+2sqrt(77/20)]/4 and r2=[5-2sqrt(77/20)]/4

So my new equation is (F)(C)=(D) where E and D are the same matrices as before and F is R1=(5/4-r1 3/4) and R2=(3/4 5/4-r2).

Now I think I need to observe the relation between E1 and E2; however, I do not see the relation - one does not appear to be a multiple of the other to me. Did I make a mistake?

Thanks

What is this big E? I don't get all your notation.

In any case, it should be clear that this matrix equation is two equations in the components of x, so you can just solve them individually with algebra and then put them back together.

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 Post subject: Re: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 18:58:41 UTC
 S.O.S. Oldtimer

Joined: Fri, 30 Oct 2009 16:33:10 UTC
Posts: 261
Oh just solve the equation - that is very obvious indeed. I am not sure why I was blind to that...

By the way, my book uses a squiggly E that I believe is a capital epsilon. The is what I was denoting by the capital "E's". I believe I defined all the other notation, but let me know if I didnt.

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 Post subject: Re: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 19:01:25 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12071
Location: Austin, TX
You've been here a while now and have over 200 posts, I think it's time to bite the bullet and learn how to use .

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 Post subject: Re: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 19:05:52 UTC
 S.O.S. Oldtimer

Joined: Fri, 30 Oct 2009 16:33:10 UTC
Posts: 261
You've been here a while now and have over 200 posts, I think it's time to bite the bullet and learn how to use .

Sorry, I have been trying. I am going to keep at it, I don't know why I am having trouble with it, but I am. I am going to try using it, but don't know if it will go too well...

Also, I was just working on this problem some more. When I try solving for E1 and E2 I get numbers as the answers. However, in an example in my book, E1 and E2 are 2x1 vectors. Do you know how they get a vector?

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 Post subject: Re: Homogeneous Linear System with Constant CoefficientsPosted: Thu, 3 Nov 2011 19:08:12 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12071
Location: Austin, TX
goteamusa wrote:
You've been here a while now and have over 200 posts, I think it's time to bite the bullet and learn how to use .

Sorry, I have been trying. I am going to keep at it, I don't know why I am having trouble with it, but I am. I am going to try using it, but don't know if it will go too well...

Also, I was just working on this problem some more. When I try solving for E1 and E2 I get numbers as the answers. However, in an example in my book, E1 and E2 are 2x1 vectors. Do you know how they get a vector?

Like I said, I didn't get your notation. Recall you can write the vector as a sum of two other vectors, there's no problem there.

As for your TeX advent, I recommend just looking at the help board when you have trouble.

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