https://file.aiquickdraw.com/mathbot/file/1727435458604rj552ijp.jpg

The eigenvalues of matrix \( C \) are:

\[
\lambda_1 = 1, \quad \lambda_2 = 4, \quad \lambda_3 = 1
\]

The corresponding eigenvectors are:

\[
v_1 = \begin{bmatrix} -0.8165 \\ -0.4082 \\ 0.4082 \end{bmatrix}, \quad
v_2 = \begin{bmatrix} -0.5774 \\ 0.5774 \\ -0.5774 \end{bmatrix}, \quad
v_3 = \begin{bmatrix} 0.3810 \\ 0.8159 \\ 0.4349 \end{bmatrix}
\]

Would you like further details on how these were computed or any other clarifications?

Here are some related questions:
1. What are the properties of symmetric matrices and their eigenvalues?
2. How are eigenvalues used in practical applications like stability analysis?
3. What is the significance of having repeated eigenvalues?
4. How do you normalize an eigenvector?
5. How does the determinant relate to eigenvalues?

**Tip:** Eigenvalues of symmetric matrices are always real numbers.

Solve for eigenvalues and eigenvectors of the given matrix C.

Find the eigenvalues and eigenvectors for the given 3x3 matrix C. This problem covers key concepts of linear algebra, including matrix operations and the characteristic polynomial. Suitable for undergraduate students learning linear algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation