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

[rrt]

what is the significance of y^2 = -4x. I know that all the lines are tangent to it, but what do I do with it.

[surfnicky1]

Blazara, you cannot give direct answers, that's basically cheating.

Surfnicky:

Blazara can give you hints but not tell you what they got or supposed to get, you're supposed to figure that out yourself.

sorry yes i appreciate that Blazara can't actually give me the answers i just wanted to know if i was on the right track

i have just actually worked out that part of what i just asked is wrong anyway

[Blazara]

Blazara, you cannot give direct answers, that's basically cheating.

Surfnicky:

Blazara can give you hints but not tell you what they got or supposed to get, you're supposed to figure that out yourself.

Ah sorry, I wasn't sure how heavy I could be, or whether that was too far.

@rrt, what section are you referring to?

[surfnicky1]

for the 3x3 section in part A i have x and y in terms of z and that there are infinite solutions - is there a way to prove this? or is that all that needs to be done?

any guidance would be appreciated!!

[Blazara]

for the 3x3 section in part A i have x and y in terms of z and that there are infinite solutions - is there a way to prove this? or is that all that needs to be done?

any guidance would be appreciated!!

Well, the fact you have them in terms of Z kind of the proof, you must of reached a row of Zeros in order to have got that answer, so you've definitely shown it, although I'm unsure if it's a proof.

Have you created a general solution to 'prove' that your answer is correct though? It doesn't demonstrate the infinity, but assures you of your answer, and hence the infinity must be true.

Heh, it's funny. I keep having to re-read my coursework to help out. Amazing how fast you let stuff slide. ;|

Edited November 3, 2010 by Blazara

[alleb5]

halloo!

i was just wondering do we need to comment on the limitations of the conjectures in both parts or just part b?

and scope is the same as laying out all the limitations right??? :P

Edited November 5, 2010 by alleb5

[Lilly7]

For the 3X3 system, don't you need three equations in the conjecture? And then how do you solve them?

[Blazara]

halloo!

i was just wondering do we need to comment on the limitations of the conjectures in both parts or just part b?

and scope is the same as laying out all the limitations right???

Yes, for higher marks you need to state limitations, scoping is slightly different, usually done so the limitations don't matter so much.

@ Lilly7 - your conjecture is what you think will happen, as in - I think they will all share a common solution, as long as they all follow an arithmetic series.

Solve them using row reduction.

[alleb5]

Yes, for higher marks you need to state limitations, scoping is slightly different, usually done so the limitations don't matter so much.

we're talking about the limitations of the conjectures right?

Edited November 6, 2010 by alleb5

[Blazara]

Yes, for higher marks you need to state limitations, scoping is slightly different, usually done so the limitations don't matter so much.

we're talking about the limitations of the conjectures right?

I'm not really sure a conjecture can have limitations? A conjecture itself is based on guesswork, the name itself implies the limitation.

Limitations should be applied to your end results, on what you found out.

[frenziedIB]

Can someone help me in part A where it says, extend your investigation to 3x3 systems whose constants exhibit the pattern seen above?

So to make 3x3 you need 3 seperate equations to solve the unknowns,

x+2y+3z=4

2x-y-4z=7

and those two equations i could derive from the equation given in the sheet,

but what about the last equation?? how do i make it ? do i just make with any pattern i want or??

i know it has no unique solution and it is infinite,, but i need the last equation.. any help??

[chrypton]

Can someone help me in part A where it says, extend your investigation to 3x3 systems whose constants exhibit the pattern seen above?

So to make 3x3 you need 3 seperate equations to solve the unknowns,

x+2y+3z=4

2x-y-4z=7

and those two equations i could derive from the equation given in the sheet,

but what about the last equation?? how do i make it ? do i just make with any pattern i want or??

i know it has no unique solution and it is infinite,, but i need the last equation.. any help??

To make your own 3x3 system you need to make 3 equations with 3 unknowns that follow the pattern you've found. Deriving a third equations from the original two won't do you any good.

[StarSecret]

Can someone help me in part A where it says, extend your investigation to 3x3 systems whose constants exhibit the pattern seen above?

So to make 3x3 you need 3 seperate equations to solve the unknowns,

x+2y+3z=4

2x-y-4z=7

and those two equations i could derive from the equation given in the sheet,

but what about the last equation?? how do i make it ? do i just make with any pattern i want or??

i know it has no unique solution and it is infinite,, but i need the last equation.. any help??

To make your own 3x3 system you need to make 3 equations with 3 unknowns that follow the pattern you've found. Deriving a third equations from the original two won't do you any good.

I too need some help on the 3x3 conjecture. Is the conjecture that we get a line solution? or a common point ? or is it the equation solution of the parametric equations? I an confused!!Pls help

[wudiwuwu]

i'm having trouble finding the vector equation of the common line in the 3x3

anybody have a hint?

also, for Part B, i got the graph to be y^2=-4x

but i only got it through trial and error

i did find the general values of y and x, but i'm stumped because i plugged in the values into the quadratic equation but my answer is ridiculous

a hint would be nice here too

[adletaY]

i'm having trouble finding the vector equation of the common line in the 3x3

anybody have a hint?

also, for Part B, i got the graph to be y^2=-4x

but i only got it through trial and error

i did find the general values of y and x, but i'm stumped because i plugged in the values into the quadratic equation but my answer is ridiculous

a hint would be nice here too

I didn't know how to do this until after I finished the IA, but I now know enough to give you a hint:

Remember, if one knows two points, one can write a vector equation for the line passing through those points.

[frenziedIB]

Can someone help me in part A where it says, extend your investigation to 3x3 systems whose constants exhibit the pattern seen above?

So to make 3x3 you need 3 seperate equations to solve the unknowns,

x+2y+3z=4

2x-y-4z=7

and those two equations i could derive from the equation given in the sheet,

but what about the last equation?? how do i make it ? do i just make with any pattern i want or??

i know it has no unique solution and it is infinite,, but i need the last equation.. any help??

To make your own 3x3 system you need to make 3 equations with 3 unknowns that follow the pattern you've found. Deriving a third equations from the original two won't do you any good.

so what pattern should the 3rd equation be ?? first equation increases in constants where in second equation it decreases,,, what about the third one?? and you mean i should follow the pattern I found in the 2x2 equation??

[wudiwuwu]

haha i got the vector equation 5 minutes after posting that

but thanks anyway ^___^

the equation of the parabola took a lot longer to realize but i got it too

its always the easiest things you overlook XP

Can someone help me in part A where it says, extend your investigation to 3x3 systems whose constants exhibit the pattern seen above?

So to make 3x3 you need 3 seperate equations to solve the unknowns,

x+2y+3z=4

2x-y-4z=7

and those two equations i could derive from the equation given in the sheet,

but what about the last equation?? how do i make it ? do i just make with any pattern i want or??

i know it has no unique solution and it is infinite,, but i need the last equation.. any help??

To make your own 3x3 system you need to make 3 equations with 3 unknowns that follow the pattern you've found. Deriving a third equations from the original two won't do you any good.

so what pattern should the 3rd equation be ?? first equation increases in constants where in second equation it decreases,,, what about the third one?? and you mean i should follow the pattern I found in the 2x2 equation??

the equations dont have to be one increasing and one decreasing.. you can take ANY 3 equations from this family of equations.. that's what makes them so special

goodluck

[amritpadda]

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?)

Part A Consider this 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.

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

Can u please help me with the last part????

[amritpadda]

Part B Consider this 2x =2 system

x+2y=4

5x-y=0.2

• Examine the constants in both equations and describe any patterns.

• Re-write the above two equations in the form y=ax+b. How are the constants a and b related? found b=-1/a

• Using technology, create a family of linear equations similar to the example shown above. On the same set of axes, display your equations. Ensure that the family of equations includes several lines with a wide range of gradients.

• Closely examine the resulting graphical display. Clearly describe any apparent graphical patterns.

• Set up and solve a general 2x2system that incorporates the patterns found above.

• Using your solution to the general system, or otherwise, provide a proof of the graphical pattern observed above.

Can someone please help me with this??

I need it till this Friday

[amritpadda]

Part B Consider this 2x2 system

x+2y=4

5x-y=0.2

• Examine the constants in both equations and describe any patterns.

• Re-write the above two equations in the form y=ax+b How are the constants a and b related? found b=-1/a

• Using technology, create a family of linear equations similar to the example shown above. On the same set of axes, display your equations. Ensure that the family of equations includes several lines with a wide range of gradients.

• Closely examine the resulting graphical display. Clearly describe any apparent graphical patterns.

• Set up and solve a general 2x2 system that incorporates the patterns found above.

• Using your solution to the general system, or otherwise, provide a proof of the graphical pattern observed above.

Can someone please help me wid this please please please????