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

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alexandercpark
 one year ago
Best ResponseYou've already chosen the best response.0i 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

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

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

RaphaelFilgueiras
 one year ago
Best ResponseYou've already chosen the best response.3if 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

maggieL
 one year ago
Best ResponseYou've already chosen the best response.0um 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?

RaphaelFilgueiras
 one year ago
Best ResponseYou've already chosen the best response.3Dim(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)

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

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

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

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

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

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

maggieL
 one year ago
Best ResponseYou've already chosen the best response.0so 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:(

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

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