1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the Basis of an Eigenspace

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Matrix A is 3x3
    1 -5 -5
    -5 1 5
    5 -5 -9
    Find basis for corresponding eigenspace when eigenvalue is -4

    a) 0 b) 1 0 c) 1 d)1 0
    1 0 1 0 0 1
    -1 1 , -1 -1 -1 , 1

    2. Relevant equations

    (A-lambda I)x=0

    3. The attempt at a solution
    (A-(-4I)= 5 -5 -5
    -5 5 5
    5 -5 -5
    that matrix times x will be equal to zero
    created augmented matrix: 5 -5 -5 0
    -5 5 5 0
    5 -5 -5 0
    find reduced echelon form of augmented matrix:
    1 -1 -1 0
    0 0 0 0
    0 0 0 0
    therefore x1=x2+x3
    and x2 and x3 are free
    vector x= x2+x3
    x2
    x3
    which can be reduced to:
    x2*1 + x3* 1
    1 0
    0 1

    For the basis of the eigenspace, I then get:
    1 1
    1 0
    0 , 1
    However, the homework question is multiple choice and this is not one of the options. What am I doing wrong?
     
  2. jcsd
  3. Apr 26, 2009 #2
    Your notation is a bit hard to deciphere... What I can make up from it is that answer b consists of the basis vectors (in a transposed notation):
    (1 0 1) and (0 1 -1)

    while your answer is the basis:
    (1 1 0) and (1 0 1)
    But you can check that these two basis span the same subspace. In other words, your answer is some linear combination of the basis of answer b, namely:
    (0 1 -1) = (1 1 0) - (1 0 1)
     
  4. Apr 26, 2009 #3
    Thanks.
    The notation did get kind of scrambled when I posted it, but thanks for your help!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the Basis of an Eigenspace
  1. Basis of eigenspace (Replies: 3)

Loading...