Find the largest Eigen value and the corresponding Eigen vector of the matrix A using Rayleigh’s power method by taking the initial vector as [ 1,0 ,0 ]^T. A = (1 – 3 2 4 4 – 1 6 3 5) with the initial vector X^((0))= [1,0,0]^T

## Problem

## Question

Find the largest Eigen value and the corresponding Eigen vector of the matrix A using Rayleigh’s power method by taking the initial vector as [ 1,0 ,0 ]^T. A = (1 – 3 2 4 4 – 1 6 3 5) with the initial vector X^((0))= [1,0,0]^T

## Topic

## Rayleigh’s Power Method Problems

- Find the largest Eigen value and the corresponding Eigen vector of the matrix by the power method given that A =[(2,0,1),(0,2,0),(1,0,2)]
- Find the dominant Eigen value and the corresponding Eigen vector of the matrix A=[(6,-2,2),((-2,3,-1),(2,-1,3)] by power method taking the initial Eigen vector as [1,1,1]
- Find the largest Eigen value and the corresponding Eigen vector of the matrix A=[(2,-1,0),(-1,2,-1),(0,-1,2) by using power by method taking the initial vector as [1, 1, 1] ^T
- Find the numerically largest Eigen value and the corresponding Eigen vector of matrix A = [(4,1,-1),(2,3,-1),(-2,1,5)] by taking the initial approximation to the Eigen vector as [1, 0.8,-0.8] ^T. Perform 5 iterations
- Using Rayleigh’ s power method find numerically the largest Eigen value and corresponding Eigen vector of the matrix, A=[(25,1,2,),(1,3,0),(2,0,-4)]
- Find the largest eigen value and the corresponding eigen vector of the given matrix A using Rayleigh’s power method taking the initial vector as [ 1,1 ,1 ]^T. A = (1 – 3 2 4 4 – 1 6 3 5) with the initial vector [1,1,1]^T
- Find the largest Eigen value and the corresponding Eigen vector of the matrix A using Rayleigh’s power method by taking the initial vector as [ 1,0 ,0 ]^T. A = (1 – 3 2 4 4 – 1 6 3 5) with the initial vector X^((0))= [1,0,0]^T