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maggieL
 2 years ago
Find a such that th subspaceSPAN{(a, 1, 1), (0, 1, 2), (1, 1, 0)} of R^3 has dimension 2.
maggieL
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0I tried but couldn't get the zeros:(

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

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

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

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

RaphaelFilgueiras
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0thanks so much! ur so patient:)

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