runef Posted May 27, 2010 Report Share Posted May 27, 2010 i've read that the lines in part b are tangent to y^2 = -4x but i have no idea about how to find it out or about the proof..would you please give me a hint?? Reply Link to post Share on other sites More sharing options...
mmannai Posted May 30, 2010 Report Share Posted May 30, 2010 Hey,umm, I came across the conjecture for part A, as mentioned previously for the 2x2, but how do I go along in "proving" the conjecture? Any tips or hints would greatly be appreciated Reply Link to post Share on other sites More sharing options...
Bishup Posted May 30, 2010 Report Share Posted May 30, 2010 In order to prove you have like a standard formula which is applicable to any matrix of that trend. So I suggest you use parameters. From their on you solve your conjecture algebraically and ultimately you'll get the same results as for any matrix that incorporates that pattern. If you need help finding the right conjecture look back into the thread and you'll encounter it.Good luck Reply Link to post Share on other sites More sharing options...
runef Posted May 30, 2010 Report Share Posted May 30, 2010 In order to prove you have like a standard formula which is applicable to any matrix of that trend. So I suggest you use parameters. From their on you solve your conjecture algebraically and ultimately you'll get the same results as for any matrix that incorporates that pattern. If you need help finding the right conjecture look back into the thread and you'll encounter it.Good luckwhat about the proof in part b..about y^2=-4x ? Reply Link to post Share on other sites More sharing options...
Bishup Posted May 30, 2010 Report Share Posted May 30, 2010 what about the proof in part b..about y^2=-4x ? How do you know the answer if you don't know the steps of the proof?Anyway same applies here write up a system of linear equations that incorporates the same pattern and make it applicable to all values that incorporate that pattern - use parameters again.Then you solve it in order to find the equation of the parabola. Did you even get to that part where you got a parabola?Proving can be any method appropriate but I prefer a formula which is in fact my conjecture and then I just prove by solving out as I would for any other system with real values. It turns out you get the same answer because the pattern is what gives the values.For me to find this proof I use a theorem. Think of quadratics - it's a parabola Reply Link to post Share on other sites More sharing options...
kg821819 Posted May 31, 2010 Report Share Posted May 31, 2010 Hey! I would really appreciate is someone could give me a hint about the graph in Part B. My entire class is confused about what we should be seeing.Oh and should I mention the patterns I see in the x and y in the solutions of two intersecting lines? Reply Link to post Share on other sites More sharing options...
miss.malhi Posted May 31, 2010 Report Share Posted May 31, 2010 Hey! I would really appreciate is someone could give me a hint about the graph in Part B. My entire class is confused about what we should be seeing.Oh and should I mention the patterns I see in the x and y in the solutions of two intersecting lines?I need help with the same thing. I'm not seeing anything significant... Reply Link to post Share on other sites More sharing options...
Kaneele Posted June 1, 2010 Report Share Posted June 1, 2010 In part B - simply draw many different lines using graph or something similar!Use different kind of coefficients, etc, following the pattern given.After some 30 or so lines, you should see the tendency Enjoy! Reply Link to post Share on other sites More sharing options...
kg821819 Posted June 1, 2010 Report Share Posted June 1, 2010 (edited) Never mind, I looked at other posts and figured it out.Thank youuuu. Edited June 2, 2010 by kg821819 Reply Link to post Share on other sites More sharing options...
giantsushi Posted June 2, 2010 Report Share Posted June 2, 2010 Hey I got the whole arithmetic pattern system going on in part A constants...but I am really confused for the conjecutre.i haveax+(a+d)y=a+2dbut aren't I meant to include the fact that all equations that follow this pattern go through (-1,2)?How do I include that in the conjecture?? =/ Reply Link to post Share on other sites More sharing options...
Kaneele Posted June 2, 2010 Report Share Posted June 2, 2010 What I did was making two types of these equations in a system.ax+(a+d)y=a+2dbx+(b+d)y=b+2dthen 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! 1 Reply Link to post Share on other sites More sharing options...
giantsushi Posted June 2, 2010 Report Share Posted June 2, 2010 What I did was making two types of these equations in a system.ax+(a+d)y=a+2dbx+(b+d)y=b+2dthen 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!Yay! thanks! I get it now thank you sooo much Reply Link to post Share on other sites More sharing options...
RAL Posted June 3, 2010 Report Share Posted June 3, 2010 Hi guys this is my first post!!I am having some trouble with the "Using technology, extend your investigation to 3x3 systems whose constants exhibit the patterns seen above."I think I have the 3x3 systems but I am not sure and can't figure out how to use technology to extend the investigation.**Spolier**I used my conjecture from the 2x2, extended it to a 3x3 and made the equations.(Select area to read)I just need a nudge in the right direction.Thanks for the guidance Reply Link to post Share on other sites More sharing options...
Kaneele Posted June 3, 2010 Report Share Posted June 3, 2010 Can you please tell me how far you are at the moment - what results have you obtained? What you could do (well, that's what I did ) is express each of the variables (x; y; z).One of the most popular ways to use technology at this point for my class was using our calculators; try to read about 'matrixes' and 'vector equation of line'. They will most probably hint you in the right direction! Reply Link to post Share on other sites More sharing options...
RAL Posted June 3, 2010 Report Share Posted June 3, 2010 I have finished the fourth bullet in Part A and I am starting the fifth bullet. Technically I already have a conjuncture for the 3x3 system, but since I cannot figure out how to use technology to get my 3x3 system. I looked at the vector stuff in the book but I when I plug in a 3x3 matrix and try to find the inverse it says it is singular so I am still stuck...Maybe I am just looking at this the wrong way...My conjecture also uses x,y,z and follows the same trend as the 2x2. This is what I came up with: ax+(a+d)y+(a+2d)z=a+3d.Thanks for your patience and help Reply Link to post Share on other sites More sharing options...
Kaneele Posted June 3, 2010 Report Share Posted June 3, 2010 If I remember correctly, you shouldn't have made a general conjecture about 3x3 or solve the general conjecture, right?Then all you need to do is solve a 3x3 system, having the pattern, (I solved 2 to show that both of them give the same results) which is take three equations, following the pattern and put them in a system. Then, try to transform them, so you can express values of x, y and z. HINT: try to express y and x via z and z via x. Then you will be able to use this vector equation of line afterwards. I hope this helped in any way at all. Reply Link to post Share on other sites More sharing options...
giantsushi Posted June 5, 2010 Report Share Posted June 5, 2010 (edited) How do you come up with a conjecture for Part B? i found the pattern and everything... plus my friend told me to use a quadratic formula to prove the conjecture. Can someone give me a little hint?Oh plus I have real trouble trying to prove my conjecture for the 3x3 part as well... Edited June 5, 2010 by giantsushi Reply Link to post Share on other sites More sharing options...
mohit Posted June 10, 2010 Report Share Posted June 10, 2010 (edited) Could you please elborate...im in dire conditions....i have a day left and only the 3x3 part left to do Edited June 10, 2010 by mohit Reply Link to post Share on other sites More sharing options...
paraguay Posted June 14, 2010 Report Share Posted June 14, 2010 Can someone please help me with proving the 3x3 systemi already know that there are always infinite solutions, i can even get the parametric solutioni just dont know how to prove that there will always be infinite solutionsssplz plz plz plz help Reply Link to post Share on other sites More sharing options...
lostfan123 Posted June 15, 2010 Report Share Posted June 15, 2010 (edited) Can someone please help me with proving the 3x3 systemi already know that there are always infinite solutions, i can even get the parametric solutionWhat 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? Edited June 15, 2010 by Aboo No text speak! Reply Link to post Share on other sites More sharing options...
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