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 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]

Question

Question

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]

Topic

Rayleigh’s Power Method

Rayleigh’s Power Method Problems

  1. 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)]
  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]
  3. 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
  4. 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
  5. 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)]
  6. 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
  7. 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

 

This Post Has 2 Comments

  1. Uday June 25, 2023 Reply

    Ey using power method All the eigen values and the corresponding eigen vector for and the corresponding eigen vector for `A= 1 -3 2 4 4-1 6 3 5 `
    I request to send answer for this question

    1. admin June 28, 2023 Reply

      Hi Uday,

      Thank you for reading our website.

      The answer for your requested question is solved and added in this page. Please check to this page.

      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

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