anonymous
  • anonymous
Find a such that th subspace-SPAN{(a, 1, 1), (0, 1, 2), (1, -1, 0)} of R^3 has dimension 2.
Linear Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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
anonymous
  • anonymous
I tried but couldn't get the zeros:(
anonymous
  • anonymous
|dw:1372827825197:dw|

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anonymous
  • anonymous
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
anonymous
  • anonymous
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?
anonymous
  • anonymous
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))=n-r (number of free variables)
anonymous
  • anonymous
dimension is the number of vectors in a basis
anonymous
  • anonymous
the third column is the linear combination of the first two ones
anonymous
  • anonymous
if a =-1/2, then the column space is spaned by(1,-1,0) and (0,1,2)
anonymous
  • anonymous
does that mean: if it has dimension 3, there can't be any zero rows?
anonymous
  • anonymous
in this case yes
anonymous
  • anonymous
so a would be -1?
anonymous
  • anonymous
if a =-1 then the dim(C(A))=3 and the nullspace contains only zero vector
anonymous
  • anonymous
C(A)=R³
anonymous
  • anonymous
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:(
anonymous
  • anonymous
I'm not*
anonymous
  • anonymous
yes
anonymous
  • anonymous
thanks so much! ur so patient:)
anonymous
  • anonymous
you are welcome

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