(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]

A = \left( \begin{array}{ccc}

2 & 0 & -1 \\

4 & 1 & -4 \\

2 & 0 & -1 \end{array} \right)

[/itex]

Find the eigenvalues and corresponding eigenvectors that form a basis over R^{3}

2. Relevant equations

3. The attempt at a solution

OK so I've found the characteristic polynomial: -λ(λ-1)^{2}

so I know my eigenvalues are 0,1,1

Then to find the eigenvectors I sub the eigenvalues in to the matrix A - λI

[itex]

A - 0I = \left( \begin{array}{ccc}

2 & 0 & -1 \\

4 & 1 & -4 \\

2 & 0 & -1 \end{array} \right)

[/itex]

then I solve:

2x -z = 0

4x + y -4z = 0

z = 2x

y = 4x

so my eigenvector is (1,4,2)

[itex]

A - 1I = \left( \begin{array}{ccc}

1 & 0 & -1 \\

4 & 0 & -4 \\

2 & 0 & -2 \end{array} \right)

[/itex]

x = z

so the eigenvector is (1,0,1)

Now I'm out of new eigenvalues to substitute. How do I find the last eigenvector?

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# Homework Help: Finding a basis of eigenvectors

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