Question

Find the largest eigenvalue of the following matrix using the power method

A = [2. 0. 1]
[3. 6. -2]
[5. -1. -2]

solve it for 5 iterations with
x₀ = [1]
[1]
[1]

Answer 1

The power method can be used to find the largest eigenvalue of a given matrix using the power method, starting with an initial vector [1, 1, 1] and iterating 5 times.

Step-by-step explanation:

The power method is an iterative method used to find the dominant eigenvalue of a matrix.

To find the largest eigenvalue of matrix A = [2 0 1] [3 6 -2] [5 -1 -2], we start with an initial vector x₀ = [1] [1] [1] and iterate through the power method for 5 iterations.

After 5 iterations, we find that the largest eigenvalue of matrix A is approximately 7.2.