(d) [10 MARKS] Let H be a path graph on 3 vertices. The eigenvalues of the adja- cency matrix of A are -√2, 0 and √2. Use this information to compute the normalised eigenvector centrality of each node in H.

Q: and find the corresponding eigenvector.

A: λ is an eigen value if we have Av=λv for some v non-zero.v is called eigen vector.

Q: Compute the characteristic polynomial of 16 17 and use it to get the eigenvalues.

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Q: F be eigenvectors of the matrix A which correspond to the eigenvalues A₁ = -3 and X = 2,…

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Q: Let A = -1 -i a. Find the characteristic polynomial. b. Find the eigenvalues. c. Find the…

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Q: The characteristic polynomial of the matrix A= 1 4 -1 is (A-2)(X - 5)². -1 -1 4 a) Find the…

A: As per your request I have solved first subpart.

Q: 3. The characteristic polynomial of the matrix A = -1 4 -1 4 -1 -1 is (A − 2)(X - 5)². a) Find the…

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Q: Let. A be an eigenvalue of an n x n matrix A. Show that. 1² -3 is an eigenvalue of 31

A: Given :  λ is an eigen value of an n×nmatrix  A . We have to prove that  λ2-3 is an eigen value of…

Q: Find the characteristic polynomial and the eigenvalues of the matrix : State the multiplicity of…

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Q: Let A be a diagonalisable n x n matrix with eigenvalues A1, 2, · · , An Prove that det(A) did2 · . ·…

A: Diagonalisable matrix: A n×n matrix A is said to be diagonalisable if there exist a non-singular…

Q: Let A be a Hermitian matrix. Show that all its eigenvalues ​​belong to the real axis.

A: See proof below

Q: Explain how to find a basis for the eigenspace associated to the eigenvalue -4 in the matrix -5 2 -4…

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Q: Q6. Find eigenvalues and associated eigenvectors for each matrix. [-1 4 -1] b) A = 0 1 0 03-21 a) A…

A: Given  A = 8-63-1                      The characteristic equation of A is…

Q: Find all of the eigenvalues of the matrix A over the complex numbers C. Give bases for each of the…

A: The answer is given below.Explanation: