(c) The QR iteration with shifts for computing the eigenvalues of a matrix A € R™×n takes the form 1 Ho = U" AU (initial reduction to upper Hessenberg form) 2 for k = 1, 2, . .. H – HRI =:QµRp (QR factorization, µk possibly complex) H41:= RµQk + HkI 3 4 5 end (i) Show that each iteration represents a similarity transformation. (ii) Define an upper Hessenberg matrix and explain why we begin by reducing A to upper Hessenberg form.

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A: Given matrix is A = -1320,  A2 = 7-3-26

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A: t used when the matrix is not diagonalisable.

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A: Consider the given difference equation.

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A: Please see the below picture for detailed solution.

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Q: Q5/ Find the eigenvalues for matrix A [1 0 -11 1 2 1 2 3 A= L2

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A: and corresponding eigen vector is  and corresponding eigen vector is

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Q: 23.2 For each of the following n × n matrices, find n eigenvalues and their eigenvectors. Try to…

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Q: 7.' Given A Find the eigenvalues and eigenvectors of matrix A

A: Use the definition of eigenvalues and eigenvectors to solve this problem.