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Homework Help: Linear algebra help

  1. Feb 15, 2014 #1
    1. The problem statement, all variables and given/known data

    Calculate the eigenvalues and eigenvectors of the matrix:
    $$ A= \begin{bmatrix}
    3 & 2 & 2 &-4 \\
    2 & 3 & 2 &-1 \\
    1 & 1 & 2 &-1 \\
    2 & 2 & 2 &-1
    \end{bmatrix} $$

    2. Relevant equations


    3. The attempt at a solution

    I've found the eigenvalues, but what disturbes me, is that I can't find a way to make the determinant triangular, as to find the values faster. Can anybody see a way to do that?
  2. jcsd
  3. Feb 15, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    You wouldn't make the determinant triangular, the determinant is just one number.

    You can make the matrix triangular by row-reduction:
    - number the rows top to bottom 1-4.
    - reorder the rows: 3-2-4-1 --> 1-2-3-4
    - after that the row-reduction to upper-triangular form should come easily.

    You probably want to do this for each eigenvalue to find the eigenvectors - so the best order for the rows will be different each time.

    You want to try this for the eigenvectors - consider:
    Last edited: Feb 15, 2014
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