Infinite Solutions

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Find the value of a for which there are infinitely many solutions to the equations:







How can I do this? These parameters chapters seems pretty obscure to me. :idiot2: If it helps you can use matrices. Thanks

[cara.mel]

There are infinite solutions if two of them are the same line. That's all I remember, no idea how to do it anymore =P
I also remember that you may need to actually know it for a multi choice question x_x

[Mao]

I dont see how i can solve that by hand (just yet)...

but if you have a TI-89T, then use rref(matrix), u should know that right??



yields the result



note: you can arrive at this with some pretty hectic substitution and those alike...

and then i'm lost...

[cara.mel]

I don't know that Mao =P

This question is really annoying me, because I know I used to be able to do it. I can go find my methods stuff and look for it, but I think my first post has the general idea. That is same line = infinite solutions, random paralell lines = no solutions, anything else = 1 solution. Except that is all for 2 equations, I don't remember what to do with 3

Edit, yeah ignore me, that is all for 2 equations. *pissed off at this* =)
I even found my photocopied chapter from the methods cas book (we had to live with the normal methods book, go guinea-pig-ness)

[dcc]

CAS is for mathematicians who cant add in their head.

(I should of done CAS)

edit: btw I tried those 'hectic substitutions' but I'm not sure how to figure out if a line in three dimensions is parallel or even how to figure out the graident of a line in three dimensions (imagine like m = rise / run / SIDEWAYS WTF LOL)

[Mao]

I don't know that Mao =P

This question is really annoying me, because I know I used to be able to do it. I can go find my methods stuff and look for it, but I think my first post has the general idea. That is same line = infinite solutions, random paralell lines = no solutions, anything else = 1 solution. Except that is all for 2 equations, I don't remember what to do with 3

same here...

there is a way with n variables.... but i really forgot how to do it

CAS is for mathematicians who cant add in their head.

(I should of done CAS)

edit: btw I tried those 'hectic substitutions' but I'm not sure how to figure out if a line in three dimensions is parallel

i thought in 3D they were planes.... ?? and intersections of planes are curves (hence infinite solution)
and then they'd have points touching (turning points)

edit: oh wait, that's 2 relations in 3D, 3 relations should be SHITLOADS more complicated...

[dcc]

man seeing this, im glad I didn't do CAS, seems tedious (harder to get good scores as well)

[dcc]

I don't know that Mao =P

This question is really annoying me, because I know I used to be able to do it. I can go find my methods stuff and look for it, but I think my first post has the general idea. That is same line = infinite solutions, random paralell lines = no solutions, anything else = 1 solution. Except that is all for 2 equations, I don't remember what to do with 3

same here...

there is a way with n variables.... but i really forgot how to do it

CAS is for mathematicians who cant add in their head.

(I should of done CAS)

edit: btw I tried those 'hectic substitutions' but I'm not sure how to figure out if a line in three dimensions is parallel

i thought in 3D they were planes.... ??

well im assuming the x-y-z like i-j-k in spec

[cara.mel]

man seeing this, im glad I didn't do CAS, seems tedious (harder to get good scores as well)

I really didn't have a choice. Year 11 methods class turned into guinea pigs ftl


To solve the question, the only thing I have thought of is trying to get 2 equations that are the same. Otherwise, a=2 could be possible. I really dont know *headdesks*

[dcc]

man seeing this, im glad I didn't do CAS, seems tedious (harder to get good scores as well)

I really didn't have a choice. Year 11 methods class turned into guinea pigs ftl


To solve the question, the only thing I have thought of is trying to get 2 equations that are the same. Otherwise, a=2 could be possible. I really dont know *headdesks*

Guinea Pigs

well.
from what Mao got from his calculator, i assume that means:





And its obvious that:



so those two solutions are parallel? lol

[Mao]

lol
i was procrastinating and i got the solution by hand now as well
but it doesnt get anywhere....

btw wouldnt the final matrix need to be:

??

[Mao]

Another wild dab:

solving for the intersections between the equations:





















PS: i know the answer is (graphed it in 3D with 89T) just dont know why....

[dcc]

ah i see where this is going!

Now, taking the F-integral-SWAP of that matrix, we arrive at:




QED

[cara.mel]

dcc, I have no idea what that means

Mao: I thought the special matrixes were like
1 0 0
0 1 0
0 0 1
No idea what that means any more xD

Your wild attempts are about where I got up to before I gave up

[Mao]

dcc, I have no idea what that means

Mao: I thought the special matrixes were like
1 0 0
0 1 0
0 0 1
No idea what that means any more xD

Your wild attempts are about where I got up to before I gave up

yeah, but that's for distinct solutions
for infinite solution i thought there has to be a row of "0 0 0" and such?