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Atomic Boo

By Atomic Boo
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Supergrunch Newbie

Supergrunch

Posted
Posted

Right, I need help on this one:

 

(in case my ascii treatment isn't obvious, M is a matrix)

 

M = (k 3)

____(0 2) , where k is not equal to 2.

 

By finding and solving the characteristic equation, I've found the eigenvalues to be k and 2. However, the problem comes in when I try to find a corresponding eigenvector to the eigenvalue k.

 

I get:

 

ka + 3b = ka

2b = kb

 

So I think b has to equal 0, but how do I find the possible values of k?

Ginger_Chris Newbie

Ginger_Chris

Posted
Posted

Ok, from what you've said:

for eigenvalue 2; a=(-3/(k-2)), b=1 (completely not normalised)

for eigenvalue k; a=1, b=0 (normalised, a=anything b=0)

 

the eigenvector corresponding to eigenvalue=k comes from that you get b=0, then you get ka=ka. so a can equal anything, and so can k, it will hold true (except k=2 because then b doesn't = 0)

 

both of these hold for any value of k (except obviously k=2). What exactly are you trying to find out? the possible values of k are anything except 2. but that was given un the question. I dont think you can narrow it down anymore.

Supergrunch Newbie

Supergrunch

Posted
Posted
Ok, from what you've said:

for eigenvalue 2; a=(-3/(k-2)), b=1 (completely not normalised)

for eigenvalue k; a=1, b=0 (normalised, a=anything b=0)

 

both of these hold for any value of k (except obviously k=2). What exactly are you trying to find out? the possible values of k are anything except 2. but that was given un the question. I dont think you can narrow it down anymore.

The question gives me the matix and asks me to find the eigenvalues using the characteristic equations and example eigenvectors.

 

How did you solve?

 

I was doing Ma = (lambda)a, where a is the eigenvector and lamda the corresponding eigenvalue.

 

However, using this method, I get a corresponding eigenvector for when lambda = 2 as (2+k)

_________________________________________________________________________(3 )

 

This is wrong- it disagrees with you and the answers.

Ginger_Chris Newbie

Ginger_Chris

Posted
Posted

using the same equation as you, for lambda=2, the equations are:

ka+3b=2a

2b=2b (b equals anything you want)

 

a(k-2)+3b=0

a=3b/(2-k)

 

I just set b as 1, so i got a=(3/(2-k) , 1), but you can set it to something to make things easier. if you set b=(2-k) then you get a=(3, (2-k))

 

on an unrelated note, could someone code in an easier way to write vectors in this forum?

Eenuh Newbie

Eenuh

Posted
Posted

Alright, weird question, but it's for art stuff in school. =P

 

We have to create a design for a tattoo, and now first they want us to look up all sorts of different tattoos and the origins of it and stuff like that. Anyone who knows any good sites about tattoos with a lot of information?

 

I'm just posting this here cause some people might be bored and looking for something to do, and this isn't all that boring to help out with. =P

Supergrunch Newbie

Supergrunch

Posted
Posted
using the same equation as you, for lambda=2, the equations are:

ka+3b=2a

2b=2b (b equals anything you want)

 

a(k-2)+3b=0

a=3b/(2-k)

 

I just set b as 1, so i got a=(3/(2-k) , 1), but you can set it to something to make things easier. if you set b=(2-k) then you get a=(3, (2-k))

 

on an unrelated note, could someone code in an easier way to write vectors in this forum?

Ah, thanks. This whole eigen thing is confusing... What's amusing is that our maths teacher couldn't believe that we didn't understand it at first.

 

Could you run it through for lamda = k?

 

EDIT: Also, what does normalised mean?

Ginger_Chris Newbie

Ginger_Chris

Posted
Posted

If lambda = k

a.k + 3b = k.a

2b=k.b (as k cannot = 2, b must =0)

 

if b=0

a.k=a.k

so a = anything you want.

 

that gives a=(anything you want, 0)

 

a normalised vector is one that has length of 1 (ie sqrt(a^2 + b^2)=1 for a 2D vector. so the normalised version of (x,0)=(1,0).

other examples, if you had (x, -x) then the normalised vector would be (1/sqrt(2))*(1 , -1).

 

I know what you mean about this whole eigenvector/value/function thing, took me ages to get it. Didn't help that the first time we did it was for 2nd order coupled differential equations (first year uni), it didn't make any sense at all until we saw it for matrices and even then it took a while for it to sink in because we were so confused after the differentials.

Stick with it, eigenvalues/vectors are very useful, especially in quantum mechanics.

Supergrunch Newbie

Supergrunch

Posted
Posted
If lambda = k

a.k + 3b = k.a

2b=k.b (as k cannot = 2, b must =0)

 

if b=0

a.k=a.k

so a = anything you want.

 

that gives a=(anything you want, 0)

 

a normalised vector is one that has length of 1 (ie sqrt(a^2 + b^2)=1 for a 2D vector. so the normalised version of (x,0)=(1,0).

other examples, if you had (x, -x) then the normalised vector would be (1/sqrt(2))*(1 , -1).

 

I know what you mean about this whole eigenvector/value/function thing, took me ages to get it. Didn't help that the first time we did it was for 2nd order coupled differential equations (first year uni), it didn't make any sense at all until we saw it for matrices and even then it took a while for it to sink in because we were so confused after the differentials.

Stick with it, eigenvalues/vectors are very useful, especially in quantum mechanics.

Right, now I get it, many thanks. Our course doesn't really use eigenvectors/values, they just got stuck on the end because someone thought that people doing further maths A2 should know what they are... So ultimately, we have to find them, and not much else. Oddly enough, I find this easier for 3x3 matrices...

MoogleViper Newbie

MoogleViper

Posted
Posted
"Pollution from cars and litter is ruining the fantastic park, trees are dying and cliff faces are crumbling" or something like that.

 

 

Thanks but I think I'll need a little more than that.

 

 

If anyone here needs help in Irish (!) let me know :)

 

 

Once the end of the rainbow was in the field next to my house. I ran down to it but everytime I got there it jumped either a few metres in front or behind me. More importantly there was no pot of gold. Was I at the wrong end or something?

 

 

 

 

Sorry

Supergrunch Newbie

Supergrunch

Posted
Posted
Chiisai poteto o hitotstu to oukii koura o futatsu kudasai

 

What does chiisai and oukii mean again? Grungey?

chiisai- small

and I think you mean ookii - big.

 

I would like one small potato and 2 big kouras. (dunno what that is)

 

dabookerman Newbie

dabookerman

Posted
Posted
chiisai- small

and I think you mean ookii - big.

 

I would like one small potato and 2 big kouras. (dunno what that is)

 

AHHHH, yes, i was wondering why i couldnt find that in my exercise book. Kora (Extended O) Cola.

Cube Community Regular

Cube

Posted
Posted

Does anyone know anything about scientific errors? (as in the "plus/minus" value after numbers). I've got homework, and lad work with them involved, and I don't have a clue about them.

Supergrunch Newbie

Supergrunch

Posted
Posted
I need help on my maths, were doing this new online homework crap and i dont get it...... heres Q1 / 2 ... i need 70% to "pass", which meens not got a detetion and a bettering.

 

untitledkt1.th.gif

 

Q3/4

 

vcm3.th.gif

 

So, have you already done question one?

 

Anyway, question 1/2:

 

y^2 + 4y + 9 = -3y -1

y^2 + 7y + 10 = 0

(y + 5)(y + 2) = 0

y = -5 or -2

 

As for the others, you just need to know that the general equation is ax^2 + bx + c = 0... I'm not going to plug values into the equation for you.

Ashley Community Regular

Ashley

Posted
Posted
Alright, weird question, but it's for art stuff in school. =P

 

We have to create a design for a tattoo, and now first they want us to look up all sorts of different tattoos and the origins of it and stuff like that. Anyone who knows any good sites about tattoos with a lot of information?

 

I'm just posting this here cause some people might be bored and looking for something to do, and this isn't all that boring to help out with. =P

 

PM Mokong, he has tats.

flameboy Newbie

flameboy

Posted
Posted

I posted this once already, got locked lol, just gonna bung this in here, desperatly need any kind of creative writing it really doesn't matter what it is, just need to help.

 

Project Brief

 

My name is Adam Ducker and I am a BA English Studies student at Sheffield Hallam University. I am currently studying in my third and final year and one of my modules is called Literary Editing. For this module I have to carry out a Research Project so I can display literary editing skills to gain an assignment grade that will count towards my final degree.

 

My chosen project is below. Please take the time to read it and hopefully you decide to submit a piece to help my cause.

 

Task

 

I am looking for submissions to go on my website. These submissions will be submitted via a forum (http://getwriting.proboards59.com/) , which will ultimately be linked to the website. I will then go through the process of accessing them before putting what I deem to be the best of that selection on the website. The submissions can be anything from a short story, a poem, an essay, a review etc…

 

I will then assess the submissions on the following criteria:

 

• Originality: a piece of work that does not reproduce or copy anything and offers a fresh and innovative story. (in the case of reviews and essays this does not apply as much)

• Reading Experience: Stories that deliver an enjoyable reading experience, this is second only to the need for originality, whether its through a stories humour, its vivid imagery or any other methods that make for a good read...

• Technical Accuracy: Whilst the aim of this project is to encourage reading of webzines and the writing of material for it, but correct grammar, spelling, punctuation is still an important part of a story

 

All of the submissions will be online on the sites forums.* The best selection from each given category will put up on the website, which will be regularly updated to incorporate any new material.

 

.

 

 

*To make a submission it is not necessary to become a member as guests can post, there is however a chat section for members to chat on.

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