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anonymous
 one year ago
Do the three lines 2x1 + 4x2 + 4x3 = 4, x2  2x3 = 2, and 2x1 + 3x2 = 0 have at least one common point of intersection? It's linear algebra, and has to do with determining the consistency of systems. Like a matrices problem, the 1 2 and 3 represent rows, not exponents.
anonymous
 one year ago
Do the three lines 2x1 + 4x2 + 4x3 = 4, x2  2x3 = 2, and 2x1 + 3x2 = 0 have at least one common point of intersection? It's linear algebra, and has to do with determining the consistency of systems. Like a matrices problem, the 1 2 and 3 represent rows, not exponents.

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tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0Have you considered a determinant?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hi rvc, I know a little about matrices since we just started going over them, but this one has thrown me for a loop.

rvc
 one year ago
Best ResponseYou've already chosen the best response.1equations are consistent if the determinant equals to zero

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so how do I make that happen? I was sick and missed the lecture, so I'm a bit lost. I sorry for bothering you. _;

rvc
 one year ago
Best ResponseYou've already chosen the best response.1do you remember how to find determinant?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, not really. I'm sorry.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I missed it. How do I find the determinant?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hm... So how does that translate into my word problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if we break it down into a matrices 2 4 4 4 0 1 2 2 2 3 0 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But I'm not quite sure I understand how the other numbers within the matrices are broken up to be multiplied(?) by either a11 a12 or a13

rvc
 one year ago
Best ResponseYou've already chosen the best response.1atm i need to go. i have my exam in the next hour. all the best and sorry to leave you in between this problem. i m sure @mathmate will help you. :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hey have you figured out how to take a determinant yet

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope, I have not. Do you have any time to help me figure out how to do it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow! That'd be great. I'm trying to work through the problems in the book for the lecture I missed but I'm kind of lost.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay basically to start off, you have an equation which is a linear function of 3 variables

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for example 1x+2y+3z=5 lets say this equation instead of x1,x2,x3

dan815
 one year ago
Best ResponseYou've already chosen the best response.1have you seen equations like this before its the qeuation of a plane in 3d space

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, a long time ago. It's been a while since I've had to work through anything like this though.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay i see well dont worry

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now how about a gradient have you heard about gradients or normal vectors to planes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nope. I have not dealt with that. We're just starting out the school year with matrices.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay well then for now i cant fully explain to you why this matrix method is working, but lets just go through the determinant

dan815
 one year ago
Best ResponseYou've already chosen the best response.1a non zero determinant means that all 3 of your systems are independant of each other meaning they are not parallel or one of the system is not a combination of the 2 remaining systems

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's okay! I appreciate your willingness to explain!

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay we dont really care about the constant term for now, again this has something do with the normal vectors how they wont depend on the constant

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so your matrix is the constants of all the coefficceints in order

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright. So we break it up into a matrix... 2 4 4 4 0 1 2 2 2 3 0 2

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we dont care about the constants in this case

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, so just the first three columns then.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yeah the numbers infront of variables only

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now to take a determinant of a matrix

dan815
 one year ago
Best ResponseYou've already chosen the best response.1first u learn to take the determinant of 2 by 2 matrix

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you take the determinant.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1this is the determinnat of 2 by 2 matrix

dan815
 one year ago
Best ResponseYou've already chosen the best response.1difference* of the product of the diagonals in that order

dan815
 one year ago
Best ResponseYou've already chosen the best response.1we will use this to take the determinant of 3by3 matrix

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. How would you combine a 3 by 3 though? A B C D E F G H I... _> AEBD, BFCE, DHEG, EIFH?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1do get the mini determinants from the big determinant what you do is cover this way

dan815
 one year ago
Best ResponseYou've already chosen the best response.1just watch that its a lot better

dan815
 one year ago
Best ResponseYou've already chosen the best response.1since the determinant is non zero you can conclude there will be only 1 intersection as they are all independant

dan815
 one year ago
Best ResponseYou've already chosen the best response.1because if u look at 3 planes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow... Thank you so much! That's amazing! It makes a lot of sense, way more than I thought it would. This is a great addition to my notes!

dan815
 one year ago
Best ResponseYou've already chosen the best response.1now if u throw in another plane, that means u are really checking the intersection of a line and a plane

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so if that plane is independant that means it will be a line passing through a plane so just a point

dan815
 one year ago
Best ResponseYou've already chosen the best response.1if the plane was not independant that means the line also belongs in that plane, which means the plane stated is actually redundant which is why ud get a 0 determinant, that wont really make sense yet but ya something to keep in mind for later

dan815
 one year ago
Best ResponseYou've already chosen the best response.1just know the formal definition of independance

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, what else would you like to explain. I'm not leaving until you're finished ^_^. I just "fanned" you and wrote what I hope will be a glowing testimonial of your efforts.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1basically this a bunch of vectors are said to be linearly independant, if there is no way to do add them or some factor of them up together to end up with 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I will make sure to add the formal definition of independence in my notes as well, so that I remember it for the next lecture.

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for example v1,v2 linearly independant if av1+bv2=0 only happens when both a and b are 0 which is the trivial case, or basically taking nothing to get nothing

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yep basically the definition in there is the same thing not stated for all sizes of vectors

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you can have v1,v2,v3...vn and they all independant if a1*v1+a2*v2+..._an*vn=0 the only solution is that a1,a2,a3...an are all 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1if that is the only solution, meaning taking nothing to get nothing, everything else doesnt product 0 that means they are lienarly independant

dan815
 one year ago
Best ResponseYou've already chosen the best response.1it is is easy to see somthing like this when u talk about orthogonal vectors which are vectors than are as indepednant as possible of each other

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for example if u take a vector in the x direction and another vector in the y direction, theres no way to add them to get 0,

dan815
 one year ago
Best ResponseYou've already chosen the best response.1once u have the existance of a vector in x, how can you even add some vector in the y direction to make it go back to 0

dan815
 one year ago
Best ResponseYou've already chosen the best response.1good luck with this stuff

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you! If nothing else, this experience has taught me to never get sick ever again. That will be the day lecture will be over something I don't understand.
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