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

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alexandercparkBest 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
 9 months ago

maggieLBest ResponseYou've already chosen the best response.0
I tried but couldn't get the zeros:(
 9 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
dw:1372827825197:dw
 9 months ago

RaphaelFilgueirasBest 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
 9 months ago

maggieLBest 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?
 9 months ago

RaphaelFilgueirasBest 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)
 9 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
dimension is the number of vectors in a basis
 9 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
the third column is the linear combination of the first two ones
 9 months ago

RaphaelFilgueirasBest 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)
 9 months ago

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

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
in this case yes
 9 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
if a =1 then the dim(C(A))=3 and the nullspace contains only zero vector
 9 months ago

maggieLBest 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:(
 9 months ago

maggieLBest ResponseYou've already chosen the best response.0
thanks so much! ur so patient:)
 9 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.3
you are welcome
 9 months ago
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