Non-Parallel Eigenvector with same Eigenvalue?

Hello,

I have been given the following matrix:

Unparseable latex formula:

A = \left[ \begin{array}{ccc}[br]3 & 1 & -1 \\[br]-1 & 1 & 1 \\[br]1 & 1 & 1 \\ [br]\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:

Unparseable latex formula:

V=\left[ \begin{array}{c}[br]1 \\[br]0 \\[br]1\\[br]\end{array} \right]

However, I am unsure on how to find the second? Any help would be greatly appreciated.

Original post by TomCadwallader

Hello,

I have been given the following matrix:

Unparseable latex formula:

A = \left[ \begin{array}{ccc}[br]3 & 1 & -1 \\[br]-1 & 1 & 1 \\[br]1 & 1 & 1 \\ [br]\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:

Unparseable latex formula:

V=\left[ \begin{array}{c}[br]1 \\[br]0 \\[br]1\\[br]\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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