IA (HL) Portfolio Type I -- Patterns Within Systems of Linear Equations

[paraguay]

Can someone please help me with proving the 3x3 system

i already know that there are always infinite solutions, i can even get the parametric solution

What do you exactly mean you can get the parametric solution, what is it?

The last point i have made my conjecture but what do i have to prove that there are infinite solutions? or parametric solution?

My point is, there are 2 parts to question. First prove why there are infinite solutions, then find the equation of the line at which all the planes intersect. So i can find the equation of the line, but i am having trouble proving my conjecture. SOMEBODYYYY HELPPPPPPP

[lostfan123]

Can someone please help me with proving the 3x3 system

i already know that there are always infinite solutions, i can even get the parametric solution

What do you exactly mean you can get the parametric solution, what is it?

The last point i have made my conjecture but what do i have to prove that there are infinite solutions? or parametric solution?

My point is, there are 2 parts to question. First prove why there are infinite solutions, then find the equation of the line at which all the planes intersect. So i can find the equation of the line, but i am having trouble proving my conjecture. SOMEBODYYYY HELPPPPPPP

So this equation of line at which all planes interesect was it based on the a,b,c,d conjecture or did you put real values and then find the equation? Also there is equation line of intersection so there has to be a unique solution, rite?

Edited June 16, 2010 by lostfan123

[cank92]

I am doing the same worksheet. But I don't know how to make a conjecture and prove it. Can anyone help?

[Kaneele]

As far as I remember for the equation of line - I wrote all the variables (x,y,z) so they were equal to a number and some kind of z value (e.g. x=z and y=4-z <-this is not as it is in the IA though).

A conjecture means you use this pattern that the part a and afterwards part b have. basically what you do, you go back to this thread and you will see some people writing it here and there (sorry, I cba to write it again). You use letters, not numbers, you write the general way of the equation.

Hope it helps in any way.

[Jacky]

Can anyone please help me with part B: The last two bullet points.

My friend told me the parabola is y^2+4x=0 but I can't prove it.

Thank you so much!

[ibforever]

hi, i really need help with part B. i know the equation of the parabola but i dont know where it fits in? does that answer the 4th bullet point?

I solved the 2x2 general system but i dont know what i am now supposed to try to prove and how to go about doing so! I would reallllllllllly appreciate any help or guidance.

Thank you.

[Aron]

Well everything is fine! i am almost done but i need to get how to prove the equation algebriacally for 2x2 in part b... i know the equation is -4x = y^2 (i lloked into previous posts but didnt help much)

i solved it using 2 equation 1. ax+ary=ar^2 and 2. bx+br1y=br1^2

i finaaly got y=r+r1 and x = -r x r1 but i still dont get that specific equation when i substitute...

any help? Am i missing something?

[Maulik]

hi guys, i have a problem in part B of the question where they ask to examine the resulting graphical patterns. i am confused right now and i don't know which patterns i should have. plz help me on that.

[setosa]

I am stuck on the 3x3 for part A

I have tried many different methods like gaussian elimination but am having trouble composing the third equation

So far I have followed the patterns from the first part:

ax+(a+1)y+(a+3)z=(a+4)

bx+(b-3)y+(b-6)z=(b-9)

However when I add a third and simply using a method it results in the same answer, am I missing something obvious or is there a better way to go about this?

Thanks =)

[killa man]

Hey guys i am stuck on the part which says

Clearly describe any patterns found above.

i found out the patterns is a relation: a sleeping parabola on the left hand side.

but what do you call this figure other wise?

what is its mathematical name?

and how do you relate the 2x2 solution to the proof of the graphical pattern?

i need these answers A.S.A.P.

cause i have to submit the IA in 5 days time..

PLS HELP!!!

[shivatrident1]

hello! i just got my maths cw recently and i almost fnished it except for part b...

i got the parabola from the graph, and i read most of ur comments and found that the equation of the parabola is y=-4x^(1/2)

but how do u get the equation?

and also, hw do u proof that all the lines are tangent to that parabola?

the proof for 2x2 i was thinking bout givin 2 equations:

ax + ary = ar^2

bx + bdy = bd^2

and i aready solved it, gettin the general equation of intersection, but is it right?

and what does the intersection has sometin to do with the lines being a tangent to the parabola?

can someone please help :) im stuck!!!

[Reem]

First of all, Hello- I'm new to the site =)

I have a few questions which I need some help on. Any advice/suggestions would be very helpful.

1. Consider the 2x2 system of linear equations=

x+2y=3

2x-y=-4

- Examine the constants in the first equation and describe any patterns. Repeat for the second equation

Where I am up to:

1st equation- 1, 2, 3 (+1)

2nd equation- 2, -1, -4 (-3)

How do I describe the patterns?

- Solve the above system. Display your solution graphically. What is the significance of the solution?

I am assuming that solving the equation means finding out x and - so this can be done through matrices or simultaneous equations right? Well, I've gone for the matrices method and it worked it! I ended up with x=-1,y=2.. And I'm done with the graph, as well, showing the intersection at (-1, 2)... WHAT'S THE SIGNIFICANCE??

- Create and solve a few more systems similar to the example above. Comment on your solutions

What exactly are similar solutions?

- Make a conjecture regarding this type of 2x2 system and prove it..

- Using technology, extend your investigation to 3x3 systems whose constants exhibit the same patterns seen above

- Make a conjecture regarding the solution to those 3x3 systems and prove your conjecture...

ANYBODY???

[hinny]

for the 2x2 use letters to denote any number in your linear equation. Solve the linear equation using letters which will give you the same answer as you would get from solving any 2x2 that follows the same pattern as example given. In the end you will 2n=y and x=-n. N being any number so could be 1 so there y=2 and x=-1.

I actually had a solid formula and for this part of the IA I did not delve into matrices since it only involves a 2x2 but I suggest you have a look at matrices later on.

Can you help me prove the 2x2 in Section B and the 3x3 in Part A. I got ideas but can formulate a good proof.

Sorry I couldn't give the direct answer but I'm not allowed to.

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

bx + (b+d)y = b + 2d

Like this?

how dyou solve it when there are more than two unknowns? since a and b cannot be the same number do we assume that it is the same when proving it?

[hinny]

What I did was making two types of these equations in a system.

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

bx+(b+d)y=b+2d

then add them each to other so that you would destroy x.

By this you will be able to prove that y=2 and then put y in the system given and check what the x value will be

Good luck!

how dyou destroy x when i add them together? can u be a bit more specific thanks it will really help me a lot !!!

[setosa]

What I did was making two types of these equations in a system.

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

bx+(b+d)y=b+2d

then add them each to other so that you would destroy x.

By this you will be able to prove that y=2 and then put y in the system given and check what the x value will be

Good luck!

how dyou destroy x when i add them together? can u be a bit more specific thanks it will really help me a lot !!!

Try making them both equal to y and then solve that way =) That's what I did

[Reem]

Hey everyone!

I'm doin' this portfolio at the moment and I'm stuck at the part that says usin' technology, extend your investigation to a 3x3 system

Can anyone help with that??

Thanks

[Bishup]

Utilise ta calculatrice You have 3 planes, but one of them is horizontal so of the line of results in your matrix will be 0. So by incorporating that you can find the individual values for X and Y bla di bla di bla. I did this IA ages ago so I don't remember exactly.

[Reem]

I tried with ax+ary=ar². Can you tell me how you did it?

Try making a system of two different equations (e.g. one would be ax+ary=ar² and the other one would be bx+bny=bn²). Try to make some transfigurations (probably using Gauss' method), until you come across x and y values, which seem like you could use them in further investigation.

Hey I'm doin' this coursework at the moment.. I'm done with part A and I'm workin' on B.. I solved the 2x2 system using Gauss method and found the values of x and y and I did come up with 2 general equations (The same two you pointed out, only different letters), the part I'm stuck at is proving that those two equations I came up with will give the same result and thus concluding that this pattern whose constants increase in a geometric progression will always give one unique result.... Can someone help me with the proof please???? What I'm up to iis: y=r+n

[Simus]

Hey, could anyone PM me a copy of this IA?

Thanks in advance

[Reem]

Hey, could anyone PM me a copy of this IA?

Thanks in advance

I've got a copy on my PC.. It's not that good, but if you zoom in, you can easily read it.. Would you like me to send it???