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Solving homogeneous system involving decimal eigenvalues

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to find the general solution of the system
    [3 5]
    [-1 -2]

    2. Relevant equations

    so to get the eigenvalues, det(A - λI)
    3. The attempt at a solution

    determinant is (3-λ)(-2-λ) + 5

    which would be λ2 - λ - 1

    so by the quadratic equation the eigenvalues are λ = 1/2 + (√5)/2 and 1/2 - (√5)/2

    but now I don't know how to reduce the matrix to get the eigenvectors?

    I think the matrix for the first eigenvalue would be
    [3-(1/2 + √5)/2) 5]
    [-1 -2-1/2+(√5)/2]

    What to do now?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 28, 2012 #2

    Mark44

    Staff: Mentor

    Do what you would normally do - row reduce the matrix, but you'll need to fix some misplaced parentheses first.

    The matrix should be
    [3- (1/2 + √5/2) 5]
    [-1 -2- (1/2+√5/2)]

    =

    [5/2 - √5/2) 5]
    [-1 -5/2 - √5/2]

    You had a few too many parentheses in your matrix.

    When the matrix is row-reduced, there should be a row of zeroes, and you can use the other row to get your eigenvector.
     
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