Eigenvalues and Eigenvectors of 3×3 Matrix Example

Task:

Find the eigenvectors and eigenvalues of the following matrix:

Solution:

To find eigenvectors we must solve the equation below for each eigenvalue:

The eigenvalues are the roots of the characteristic equation:

The solutions of the equation above are eigenvalues and they are equal to:

Eigenvectors for:

Now we must solve the following equation:

First let’s reduce the matrix:

    

This reduces to the equation:

Eigenvectors for:

Now we must solve the following equation:

First let’s reduce the matrix:

 

This reduces to the equation:

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