linear algebra help please

Guest · Post by **Guest** » Mon Feb 20, 2006 12:58 am

I need to find the difference equation to generate the following sequence:

1,3,6,10,15,21,28,36,45,55,66,78,91... (the terms are just the sums of the first n integers)

I know how to find the difference equation for a periodic sequence, but for this one I don't know what to do. Anyone do this level of linear?

Guest · Post by **Guest** » Mon Feb 20, 2006 1:15 am

ok, a friend found it, its ak+3 = ak - 3ak+1 + 3ak+2

now what is it for

1,1,2,2,3,3,4,4,5,5,6,6...

my friend wrote a program to find it by making a matrix and then "guessing" the size of the transition matrix. anyone know a better way to do this? possibly with Maple.

Post by **Pext** » Mon Feb 20, 2006 2:42 am

a_1 = 1
a_2 = 1
a_n = a_(n-2) + 1

Post by **Pext** » Mon Feb 20, 2006 2:45 am

hm... these recurrence equations are an interresting topic.

Guest · Post by **Guest** » Mon Feb 20, 2006 3:05 am

Pext wrote:a_1 = 1
a_2 = 1
a_n = a_(n-2) + 1

hmm I'm not sure that you can have scalar in the difference equation

Guest · Post by **Guest** » Mon Feb 20, 2006 3:13 am

lol i found how to do it in maple, im so dumb for not thinking about this before.

btw the diff equation for 1,1,2,2,3,3... is:

Ak+2 = -Ak + Ak+1 + Ak+2

Post by ek » Mon Feb 20, 2006 3:15 am

Mathematician

Post by **Nightshade** » Mon Feb 20, 2006 3:26 am

Pext wrote:a_1 = 1
a_2 = 1
a_n = a_(n-2) + 1

Stop helping the sorry retard, would you?

Guest · Post by **Guest** » Mon Feb 20, 2006 3:38 am

Nightshade wrote:
Pext wrote:a_1 = 1
a_2 = 1
a_n = a_(n-2) + 1
Stop helping the sorry retard, would you?

you used to help me too, remember implicit differentiation? :lub:

Post by ek » Mon Feb 20, 2006 3:39 am

LOL, funny how you accepted that you are a retard. :icon29:

Post by **Pext** » Mon Feb 20, 2006 4:16 am

Nightshade wrote:Stop helping the sorry retard, would you?

ToxicBug wrote:hmm I'm not sure that you can have scalar in the difference equation

(hint: a_(k+1) is a better notation for your ak+1 ... assuming that 'a' is the sequence and 'k+1' is the index)

btw:

a_(k+2) = - a_k + a_(k+1) + a_k+2

<=> 0 = -a_k + a_(k+1)

<=> a_k = a_(k+1)

... this is not true for your sequence.

Guest · Post by **Guest** » Mon Feb 20, 2006 4:26 am

I made a typo, its:

A_k+3 = -A_k + A_k+1 + A_k+2

Post by **Pext** » Mon Feb 20, 2006 4:37 am

ok

i now see what the difference was: you want your sequence to be described by a homogenous equation.

i.e.

A*a_k + B*a_k+1 + ... = 0

vs

A*a_k + B*a_k+1 + ... = f(k) , where f: N

R

Guest · Post by **Guest** » Mon Feb 20, 2006 4:39 am

Maybe, on the paper its just called "difference equation".

by the way, what are u studying?

Post by **Pext** » Mon Feb 20, 2006 5:44 am

maths

Guest · Post by **Guest** » Mon Feb 20, 2006 6:08 am

what kind?

Post by **SplishSplash** » Mon Feb 20, 2006 7:58 am

Argh, this is the worst kind of math.

Thank god I don't have to do this anymore. (If I managed to pass the test last week anyway)

Post by **Pext** » Mon Feb 20, 2006 11:05 am

i'll write my first test at uni today. didn't learn that much though ~ but i think, i'll pass.

today is analysis ( metric spaces , integrals , differenciations , taylor stuff )

tomorrow is linear algebra ( linear transformations , multilinear transformations, tensor product, quotient vector spaces, etc ... )

Post by **MKJ** » Mon Feb 20, 2006 11:43 am

christ. the least you can do is "help me with this please, i dont get it" rather than posting "whats the answer to so and so"

pathetic

Post by **Nightshade** » Mon Feb 20, 2006 12:25 pm

He doesn't want to understand it, he just wants an A.

Post by **YourGrandpa** » Mon Feb 20, 2006 2:07 pm

I just hope you guys can find a use for it and it all doesn't end up being a waste of time.

Post by **Ezekiel** » Mon Feb 20, 2006 2:15 pm

I remember asking my maths teacher what the point of algebra was. She was very emphatic when explaining how (like everything else in the lesson) it would be of great use in later life.

"But Miss, why don't they give you real numbers instead? It would be easier!"

I could never understand the point in algebra when I was ten, and my stance on the matter still hasn't changed eleven years later. Bar very specialist fields I fail to see how it is of use to anybody.

Post by **Nightshade** » Mon Feb 20, 2006 2:18 pm

How about solving anything that has an unknown quantity in it? You use it all the time, you just don't think about it. ToxicDud just doesn't think, period.

Post by **Ezekiel** » Mon Feb 20, 2006 2:27 pm

That is a fair point, but people who have never done an algebra question still use the same train of thought to work out an unknown quantity. It has always seemed like a rather long winded way of putting the thought process on paper to me.

I'm not one to talk to about maths though - English has always been my strong point and I both admire and wonder about those who are able to take maths at degree level. The admiration comes from them doing something that I regard as quite a hard subject choice, the wonder comes from me trying to work out why they actually bother. :icon32:

Post by **SplishSplash** » Mon Feb 20, 2006 2:35 pm

MKJ wrote:christ. the least you can do is "help me with this please, i dont get it" rather than posting "whats the answer to so and so"
pathetic

The problem with this stuff (geometrical rows, etc...) is that it's not hard to understand, but tricky to solve. Like chess.