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Portfolio Type I -- Patterns Within Systems of Linear Equations

Sunny.P

By Sunny.P
in Maths HL & Further

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chaosier

chaosier

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Hi all, I saw this thread on IBsurvival and I need some help with starting off. For Part B the pattern is quite obvious but I am having problems with the first question of Part A where it asks about the patterns and constants. Could somebody help start me off?

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Lekha

Lekha

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Posted (edited)

Hi all, I saw this thread on IBsurvival and I need some help with starting off. For Part B the pattern is quite obvious but I am having problems with the first question of Part A where it asks about the patterns and constants. Could somebody help start me off?

Part A is kinda the same thing... for Part B you should've gotten a geometric pattern with a common ratio... for Part A, it's an arithmetic pattern with a common difference... That should make it VERY clear.

However, I need help with the using technology part in both Part A & B... how do you use technology to extend your investigation to 3x3 systems for Part A? and how do you use it to create a family of linear equations? And then display the equations on the same set of axes or whatever for Part B? I'm totally confused and stuck on these two parts!!!

Edited by Lekha
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Lekha

Lekha

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Posted

Ok, now that I thought about it for Part B, I guess you'll just put in similar equation into a graphing calculator and graph it... I just don't have the thing where you can plug it to a computer and print the screen - so does anyone have any alternate methods I haven't thought of?

Anywho, I still need help on the using technology for PART A!!! It's due tomorrow and I've been working on this all yesterday... and I'm really not sure how I can use a spreadsheet or graphing calculator(the only kind of technology I really have available) for 3x3 systems - like, wouldn't that make a plane if I graphed it? Or maybe I'm thinking about it in the wrong way? Please help me get started with this!! Thanks! :P

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chaosier

chaosier

Posted
Posted

Hi all, I saw this thread on IBsurvival and I need some help with starting off. For Part B the pattern is quite obvious but I am having problems with the first question of Part A where it asks about the patterns and constants. Could somebody help start me off?

Part A is kinda the same thing... for Part B you should've gotten a geometric pattern with a common ratio... for Part A, it's an arithmetic pattern with a common difference... That should make it VERY clear.

However, I need help with the using technology part in both Part A & B... how do you use technology to extend your investigation to 3x3 systems for Part A? and how do you use it to create a family of linear equations? And then display the equations on the same set of axes or whatever for Part B? I'm totally confused and stuck on these two parts!!!

Um... in part b aren't a and b just related by their negative reciprocals?

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Lekha

Lekha

Posted
Posted

Hi all, I saw this thread on IBsurvival and I need some help with starting off. For Part B the pattern is quite obvious but I am having problems with the first question of Part A where it asks about the patterns and constants. Could somebody help start me off?

Part A is kinda the same thing... for Part B you should've gotten a geometric pattern with a common ratio... for Part A, it's an arithmetic pattern with a common difference... That should make it VERY clear.

However, I need help with the using technology part in both Part A & B... how do you use technology to extend your investigation to 3x3 systems for Part A? and how do you use it to create a family of linear equations? And then display the equations on the same set of axes or whatever for Part B? I'm totally confused and stuck on these two parts!!!

Um... in part b aren't a and b just related by their negative reciprocals?

Yes, for the second bullet in Part B that's right... but for the patterns of the constants(the first bullet) the pattern is a common ratio: like for x+2y=4 the ratio =2 since the constants increase by a factor of two. so for Part A, the pattern is a common difference, like for x+2y=3, d=1 since the constants increase by +1.

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Lekha

Lekha

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my question paper for part B doesn't ask about doing anything for 3x3 but a lot of people are talking about 3x3 so I'm wondering whether or not to do it. Apparently it's better if you include extra stuff?

The 3x3 systems question is in Part A, not B.

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runef

runef

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my question paper for part B doesn't ask about doing anything for 3x3 but a lot of people are talking about 3x3 so I'm wondering whether or not to do it. Apparently it's better if you include extra stuff?

the 3x3 mentioned here is about part A =)

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Lekha

Lekha

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isn't 3x3 just the same as the 2x2 proof, and using gaussian elimination

yes, if u used guass' method for 2x2 proof, it should be similar for 3x3... however there are other ways to prove this also.

using gaussian elimination worked for me for the 3x3, however i used substitution and basic math to prove my conjecture for the 2x2. proving the 3x3 is just a little more complicated than 2x2, since you are working with more slots in your augmented matrices - but everything should work out in the end :ban:

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chaosier

chaosier

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Hi I need some help with the ending sections of Part B where I have to prove that y=(-4x)^(1/2), I found the equation out by using some trial and error but I am completely stuck with proving it :D!!!. I've tried ax+ary=ar^2 with a separate equation bx+bny=bn^2 but the answer im getting makes no sense to me :o!!! pls help!!!

Edit: Actually they make sense as answers to patterns but they do not explain the curve.

Edited by chaosier
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Bishup

Bishup

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Posted

It's a line of solutions or an infinite amount of solutions

the conjecture is something like x-z=2 and z+y=-1 So you can't know the values.

Type it on a calculator and see.

It is a line of solutions because "you'll see when you type the matrix in your calculator"

It wasn't as algebraically easy as for the 2x2 though.

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mathnovice

mathnovice

Posted
Posted (edited)

Thanks Bishup, I got those two conjectures that you were talking about through the calculator.

As for the proving part, how should I go along doing that?

Do similar to the 2x2 and make them equal to each other?

Edit: I think I got it, no need for help anymore.

Edited by mathnovice
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chaosier

chaosier

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Anybody care to assist me in proving the graphical pattern in Part B? I've already worked out the x and y solutions in relation to different geometric ratios, and I don't know what to do next. I know that the graph should be y=(-4x)^(1/2) through trial and error

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