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Math Help - Linear Algebra..

  1. #1
    Junior Member
    Joined
    Sep 2008
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    61

    Linear Algebra..

    We were given a 3 x 3 matrix,
    1 2 0
    -1 -1 1
    0 1 1

    We are asked
    a) the characteristic polynomial of A.
    b) eigenvalues of A.
    c) the basis for each eigenspace of A.
    d) the algebraic and geometric multiplicity of each eigenvalue.

    Parenthesis are the book answers.
    I don't know what I did wrong for a & b

    a) I did the crossproduct and got -3L^3 + L^2 + L - 1 (-L^3 + L^2)
    b) L = 1,1 (L=0,1)
    c) I know how to get this, but I need the right eigenvalues...
    d) I have no idea what this means, could someone explain?
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  2. #2
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
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    The raggedy edge.
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    Exclamation

    Use Det(M-\lambda I) and find the determinant.

    The first bit is like this:

    \begin{vmatrix}<br />
{1-\lambda}&{2}&{0}\\ <br />
{-1}&{-1-\lambda}&{1}\\ <br />
{0}&{1}&{1-\lambda}<br />
\end{vmatrix}

    The expression obtained form this is the characteristic equation.

    Solving this (ie. find when the determinant=0) will give you the eigenvalues.
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