Non-Parallel Eigenvector with same Eigenvalue? Watch

TomCadwallader
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Hello,

I have been given the following matrix:

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

3 & 1 & -1 \\

-1 & 1 & 1 \\

1 & 1 & 1 \\ 

\end{array} \right]

I have found the eigenvalues are 1 and 2.

I am then asked to find two non-parallel eigenvectors of the eigenvalue 2. I have already found:

V=\left[ \begin{array}{c}

1 \\

0 \\

1\\

\end{array} \right]

However, I am unsure on how to find the second? Any help would be greatly appreciated.
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brianeverit
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(Original post by TomCadwallader)
Hello,

I have been given the following matrix:

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

3 & 1 & -1 \\

-1 & 1 & 1 \\

1 & 1 & 1 \\ 

\end{array} \right]

I have found the eigenvalues are 1 and 2.

I am then asked to find two non-parallel eigenvectors of the eigenvalue 2. I have already found:

V=\left[ \begin{array}{c}

1 \\

0 \\

1\\

\end{array} \right]

However, I am unsure on how to find the second? Any help would be greatly appreciated.
How about V=\begin{bmatrix}0\\1\\1 \end{bmatrix} \mathrm{\ or\ }\begin{bmatrix} 1\\-1\\0 \end{bmatrix}
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