mattix powers

Martin · 2007-09-22 23:24:48

in my IB sl math course i got a project concerning matrix powers. i've reached a point where i have to figure out a pattern, but i've sat here for a while without success.

any help would be awsome

http://img459.imageshack.us/my.php?image=aufzeichnenyy7.jpg

can anyone find a general pattern with the powers?

JaneFairfax · 2007-09-23 01:36:40

So the problem comes down to simply solving the simultaneous recurrence relation.

Martin · 2007-09-23 02:00:44

i'm lost i drag at math

what in the world do i havta do?

JaneFairfax · 2007-09-23 02:25:16

Im not sure what to do myself. At least Ive narrowed the problem down to recurrence relations so we dont have to keep messing about with matrices.

We have

So we have to find (if we can) a formula for the a[sub]n[/sub]s and b[sub]n[/sub]s.

Last edited by JaneFairfax (2007-09-23 02:26:38)

Martin · 2007-09-23 02:29:02

ok now i understand this part, thnx a lot

but for me the hard part is always getting a general formula.

i'll sit down and think about this though now. thnx for the help.

Martin · 2007-09-23 02:38:44

but what i have just realized is that i have to get a general formula for a matrix, not for a recurence relation.

JaneFairfax · 2007-09-23 03:47:37

Once youve solved the recurrence relation, you can plug in the formula into the matrix, because

Martin · 2007-09-23 05:02:02

well, thnx for the help. i'll see what i can do with it. But I think this is making it too complicated and it's a bit too advanced for what we're supposed to do. We're 12th Grade IB diploma math and I've never even heard of this type of stuff.

JaneFairfax · 2007-09-23 06:54:45

HAVE NO FEAR! I HAVE GOT THE FORMULA AT LAST!

Hence:

I had to discover the formulae by digging through complicated processes involving the binomial theorem. But now that I have done the hard work, its all plain sailing for you because you can use mathematical induction to prove that my formulae make sense. (I mean, I couldnt use induction myself because I didnt have any formulae in the first place but now that I have found the formulae by hook or by crook, you can use induction yourself, you lucky devil. )

Last edited by JaneFairfax (2007-09-23 06:58:41)

Martin · 2007-09-23 08:58:45

WOOHOO thnx a lot.

Martin · 2007-09-23 18:54:46

for the recurrence relations; the problem is that to find a given power, say 50, you need to know the value of the matrix at power 49 for it to work. can one generalize that even more?

Last edited by Martin (2007-09-23 19:40:23)

Math Is Fun Forum

#1 2007-09-22 23:24:48

mattix powers

#2 2007-09-23 01:36:40

Re: mattix powers

#3 2007-09-23 02:00:44

Re: mattix powers

#4 2007-09-23 02:25:16

Re: mattix powers

#5 2007-09-23 02:29:02

Re: mattix powers

#6 2007-09-23 02:38:44

Re: mattix powers

#7 2007-09-23 03:47:37

Re: mattix powers

#8 2007-09-23 05:02:02

Re: mattix powers

#9 2007-09-23 06:54:45

Re: mattix powers

#10 2007-09-23 08:58:45

Re: mattix powers

#11 2007-09-23 18:54:46

Re: mattix powers

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