Diagonalize the matrix 
2 1 -1
1 1 -2-2 1
Find A?

To diagonalize the matrix \( A \), we need to follow these steps:

1. **Find the eigenvalues** of \( A \).
2. **Find the eigenvectors** corresponding to each eigenvalue.
3. **Form the matrix \( P \)** using the eigenvectors as columns.
4. **Form the diagonal matrix \( D \)** using the eigenvalues on the diagonal.
5. Verify that \( A \) can be diagonalized by checking if \( A = PDP^{-1} \).

Let's proceed step by step.

### Step 1: Find the eigenvalues of \( A \)

Given matrix \( A \):

\[
A = \begin{pmatrix}
2 & 1 & -1 \\
1 & 1 & -2 \\
-2

Learn how to diagonalize the matrix 2 1 -1; 1 1 -2; -2 1 step-by-step. Find eigenvalues, eigenvectors, and verify diagonalization. This problem is suitable for advanced college-level students studying linear algebra.

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