Find eigenvalues and eigenvectors of a 3 x 3 matrix with example 

Let's go through an example to find the eigenvalues and eigenvectors of a 3x3 matrix. Suppose we have the following matrix \( A \):

\[ A = \begin{pmatrix}
4 & 1 & 2 \\
1 & 3 & 0 \\
2 & 0 & 2
\end{pmatrix} \]

### Step 1: Find the Eigenvalues
The eigenvalues \(\lambda\) of a matrix \(A\) are found by solving the characteristic equation:

\[ \text{det}(A - \lambda I) =

Learn how to find eigenvalues and eigenvectors of a 3x3 matrix with a detailed step-by-step example. This problem covers matrix algebra concepts, including the characteristic equation. Suitable for advanced undergraduate students studying linear algebra.

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