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maggieL
Group Title
Find a such that th subspaceSPAN{(a, 1, 1), (0, 1, 2), (1, 1, 0)} of R^3 has dimension 2.
 one year ago
 one year ago
maggieL Group Title
Find a such that th subspaceSPAN{(a, 1, 1), (0, 1, 2), (1, 1, 0)} of R^3 has dimension 2.
 one year ago
 one year ago

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alexandercpark Group TitleBest ResponseYou've already chosen the best response.0
i believe you just use some way to solve a system of equations (i would use RREF) and find a value of a such that one of those will zero out
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
I tried but couldn't get the zeros:(
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
dw:1372827825197:dw
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
if the column space has dim( 2) the rank of matrice must be 2 and the null space must have dim 1 then a=1/2
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
um I'm trying to digest this... I'm actually a bit confused with the "null space". so does dimension2 mean 2 leading 1s with 1 free variable or am i just mixing things up?
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
Dim(R(A)=C(A'))=Dim(C(A))=rank A is mxn Dim(C(A))+dim(N(A'))=m Dim(R(A))+dim(N(A))=n dim(N(A))=nr (number of free variables)
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
dimension is the number of vectors in a basis
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
the third column is the linear combination of the first two ones
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
if a =1/2, then the column space is spaned by(1,1,0) and (0,1,2)
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
does that mean: if it has dimension 3, there can't be any zero rows?
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
in this case yes
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
so a would be 1?
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
if a =1 then the dim(C(A))=3 and the nullspace contains only zero vector
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
C(A)=R³
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
so if it has dimension 3, I would have to write a=1 with the column space spanned by (1, 1, 0) (0, 1, 2) (1, 1, 1)? sry I'm so smart with this:(
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
yes
 one year ago

maggieL Group TitleBest ResponseYou've already chosen the best response.0
thanks so much! ur so patient:)
 one year ago

RaphaelFilgueiras Group TitleBest ResponseYou've already chosen the best response.3
you are welcome
 one year ago
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