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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