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Portfolio Type I -- Patterns Within Systems of Linear Equations


Sunny.P

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Hint:

x(a+d)+y(a+2d)=a+3d

or

x(a+d)+y(a+2d)+z(a+3d)=a+4d

better to do

ax + (a+d)y = a + 2d

less terms...

You will see the significance later once you solve the question. (on your x and y... WHAT'S LEFT?)

Erm.. I feel stupid for asking this, but how did you get this answer? What chapter is this from?

haha... no chapter. you only notice there are common differences and then you come up with the aforementioned form.

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are we actually supposed to write a second draft for this IA type? because my teacher said he'll be going through it and it's been ages and he didn't even mention about the IA so i'm starting to think the thing i've submitted will be the final............... :o

I'm not very sure... try to ask your teacher?

its just surprising why more than half of the world chose to do type 2, patterns of complex numbers, and am like some of the few that is doing the shadow functions! :/

does anyone of a forum that discusses about shadow functions or should i start one? :P

patterns of complex numbers is type 1. and we don't get to choose. our teachers chose.

it exists already http://www.ibsurvival.com/topic/15514-shadow-functions/

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wow! my teacher stated that we could choose any type we want for the portfolio, as long as you do atleast one.

actually you have to do two. one from type 1 and another one from type 2.

you're so lucky. I wish I could choose too, I'd choose patterns in complex numbers and modelling a functional building. sigh.

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Guest ...^....

hello everyone...

I am stuck in Part A last point.... Proving your conjecture...

My conjecture is that the solution will be the same which (-1,2) when they exhibit the same arithmetic pattern in their coefficient.

I am not sure how they want me to prove it.

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Guest ...^....

Thank Desy. Found it :)

But now I am stuck with the software I should use. I wanted to use Excel. But that would be tiring

Do anyone know, or used any other efficient and useful software.

any help is appreciated

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Guest ...^....

Anybody who is alive could help me!!!

I did a horrible mistake. My proof is not good and it is not a proof.

I am stuck with it. My portfolio is due to 3 days :read: . Someone HELP!!!! :bawling:

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Anybody who is alive could help me!!!

I did a horrible mistake. My proof is not good and it is not a proof.

I am stuck with it. My portfolio is due to 3 days :read: . Someone HELP!!!! :bawling:

Hi, You mean the proof for the arithmetic progression. I did only some notes on this IA, so I don’t think if I can help you that much. But can you give your general formula for the arithmetic progression of the coefficient in the linear equation. Just to make sure you are in the right track.

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What are you talking about? What General formula? I only wrote a statement that shows there is an arithmetic progression.

Now, I know why you couldn’t prove it, because you didn’t have the general formula.

Well, let say ax + by = c

a is the starting coefficient of the arithmetic progression

b is the second one which will be a + k

c is the last one and it will be a + k + k, which is actually a+2K

Now use these to make the formula. And then I think you will be able to find the proof easily

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Okay, I tried to do it, and here is what I got

ax + (a+k)y = a + 2k

But now I am still stuck again. I can’t find anything. Can you please elaborate?

Thank you

I can’t help you that much into details. But I think here is a big hint. Use substitution now (-1,2).

You should get what on the Left Hand Side = the Right Hand Side

And this will be your proof, it’s like 1+1=2

The LHS=RHS so it is true. You should find the same thing when you use substitution.

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urgh... that is not proving.

you have 2 equations in all your examples right? so when generalising, you also need 2 equations. use different parameters. then just solve them algebraically the way you did with your example. in the end you can cancel the parameters off and get the same solution as in your examples.

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urgh... that is not proving.

you have 2 equations in all your examples right? so when generalising, you also need 2 equations. use different parameters. then just solve them algebraically the way you did with your example. in the end you can cancel the parameters off and get the same solution as in your examples.

It is a proof, but not elegant. I have an elegant proof, but I can't help him with that because I gave him a lot of help. He didn't seem to understand what I wanted him to do. So I made him do this one. I made him insert the point of intersection in that equation to get the proof.

I know that this proof only worked because he knew the intersection point. However, the proof I have doesn't require you to know the intersection point in the first place. However, I don't think he was able to figure it out by himself "better than nothing"

I didn't do any cancelling, but what I did is some rearranging to that equation and extracted the proof that it will work for any n×n. :)

Maybe you got another proof, but mine is hundered percent correct. And I am sure of that. and I can send you a message of the proof if you want to :D

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