Eigenvalues & Eigenvectors.

  1. Find the eigenvalues and corresponding eigenvector of the matrix.
    A=
    [-4 4 8 ]
    [0 0 -10]
    [0 0 2 ]

    [1 -1 0]
    ~ [0 0 1 ]
    [0 0 0 ]

    I calculated by A = -[itex]\lambda[/itex]I

    So,

    [1-lamda -1 0 ]
    [0 -lamda 1]
    [0 0 -lamda]

    so, lamda = 0,0, and 1

    So I got

    1st eigen value: 0 eigen vector (1,1,0)
    2nd eigen value: 0 eigen vector (1,1,0)
    3rd eigen value: 1 eigen vector (1,0,0)

    1st and 2nd values were right, but third one was wrong.
    I tried several times, and I always get 1(1,0,0)

    What do i need to do ?
    thanks
     
  2. jcsd
  3. mathwonk

    mathwonk 9,682
    Science Advisor
    Homework Helper

    if you reduce the matrix, you change the eigenvalues, except for 0. don't reduce the matrix, find the characteristic polynomial of the original A.
     
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