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windsylph
Group Title
: Linear Algebra: Describe the intersection of the two hyperplanes x1 + 2x2  x3 + x4 = 8 and x1 + 3x2 + x3  x4 = 2.
 3 years ago
 3 years ago
windsylph Group Title
: Linear Algebra: Describe the intersection of the two hyperplanes x1 + 2x2  x3 + x4 = 8 and x1 + 3x2 + x3  x4 = 2.
 3 years ago
 3 years ago

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victorarana Group TitleBest ResponseYou've already chosen the best response.0
They intersecate on a plane
 3 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.0
Is there a way to get an equation for that plane?
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
You could set up the augmented matrix, row reduce to get the values and that should be the point of intersection
 3 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.0
yep I did that.. and haha seemingly im stuck on a dumb question: let a and b be free variables. my solution then is (ab+4, 2, a, b)^T. How do I express that as a span, then as an equation?
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
i get x2 = 2; x3 = x1 + x4  4; So like you said x1 and x4 are free so the span is: =(2 , 4) + x1(1, 0, 1, 0) + x4(0, 0, 1, 1) (these are vertical vectors I just cant write it on here) =(2, 4) + x1u + x4v (u and v are vectors above)
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
understand?
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
I made a small mistake: It is x3 and x4 that are free so it becomes x1=4 +x3  x4 x2 =2 which translates to... =(2 , 4) + x3(1, 0, 1, 0) + x4(1, 0, 0, 1)
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
(4, 2, 0, 0) sorry
 3 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.0
thanks, i was looking for an answer of the form span(u,v), but if that's that then that's okay. how about an equation for the plane?
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
well span(u,v) is just the span of those vectors: span{ (1, 0, 1, 0) , (1, 0, 0, 1)}
 3 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.0
oh, so (4,2,0,0)^T doesn't matter when expressing it in that form?
 3 years ago

tdabboud Group TitleBest ResponseYou've already chosen the best response.0
nope because it only depends on the free variables
 3 years ago

windsylph Group TitleBest ResponseYou've already chosen the best response.0
okay thanks. is there a way to express that as an equation?
 3 years ago
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