Problem 1. Use five iterations of the Power Method to find the eigenvector centralities of che graph P5.

Is d=2 eigen value 3. an of 3.

3) Using the Power method, obtain the largest eigenvalue and the corresponding eigenvector for the following eigenvalue problem. Stop all calculations after two iterations. Use the trial eigenvector =

Can step 2 be more elaborated upon? Specifically on how each eigenspace is found.

I try to use the eigenvalue to find eigenvector, and I've already found the relation between x and y. I can substitute x=1 and get y=-i, but the solution provided is substituting x=-1 and get  y=i. There is a problem, how can I know which value of x should I choose?

.giffgaff ← 22:52 Photo Problem 5. Consider matrix A as ^-(-2,-²) A = DO لك 37% Done Solve the eigenvalue equation and find the eigenvalues and eigenvectors of the A.

Find Eiganvalves and semapording eigenvedos of 3 Cx= to %3D 16 Į 3 -1 3

[3] [4] [¹]. Let Suppose the eigenvalues of a (3 × 3) matrix A are 2, −1/2, and 1/3, with corresponding eigenvectors Let x = []. Find the solution of the equation *k+1 = Ark for the specified o= xo, and describe what happens as ko. You may use a calculator to perform row reduction.

4.F.1 Suppose the eigenvalues of a 3 × 3 matrix A are 2, 3/5, and 2/5 with corresponding eigenvec- tors --E} --} --E} 1 2 vi = v2 = v3 = 34 For this problem you don't need to know A!! a) Describe A(v1 + 2v2 + 3v3) as a linear combination of {v1, v2, V3}. -2 b) Let æo = -5 . Describe ro as a linear combination of {v1, v2, v3}. 3 c) Find the solution of the equation ¤k+1 = Axk for the specified xo (e.g. find an explicit formula for æk in terms of the eigenvectors v;). d) As k → 00, describe the behavior of æk. (Answer both the question: does lim x exist? What can you say about the line through Tk, or the angle between rk and any other vectors.) e) As k → -0, describe the behavior of ær. (Same parenthetical.)

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