The image contains three problems. Here's a breakdown of what is visible:

1. Find Eigenvalues and Eigenvectors

   • A matrix is given: 4 & -20 & -10 \\ -2 & 10 & 4 \\ 6 & -30 & -13 \end{pmatrix}$$

   You are tasked to find the eigenvalues and eigenvectors of this matrix.

2. Reduce the quadratic equation

   • A quadratic equation in terms of $x_1, x_2, x_3$ is given: $x_1 + 2x_2 + x_3 - 2x_2x_3$ You need to reduce this equation and find its nature.

3. Verify Cayley-Hamilton Theorem for Matrix A

   • A matrix $A$ is given: 1 & 2 & 2 \\ 0 & 2 & 1 \\ 1 & 2 & 2 \end{pmatrix}$$

   You are asked to verify the Cayley-Hamilton Theorem for this matrix and show that $A^{-1}$ and $A^4$ can be calculated.

Would you like to start with a particular question or need a detailed explanation for one of them?

Here are some relative questions based on this content:

1. How do you compute eigenvalues and eigenvectors for a 3x3 matrix?
2. What is the significance of reducing quadratic equations and finding their nature?
3. Can you explain the Cayley-Hamilton Theorem and how it is applied to a matrix?
4. What role do eigenvalues and eigenvectors play in reducing matrices to canonical form?
5. How can matrix inverses and higher powers, like $A^4$, be calculated efficiently?

Tip:

For finding eigenvalues, use the characteristic equation $\text{det}(A - \lambda I) = 0$, where $\lambda$ are the eigenvalues, and $I$ is the identity matrix.