Let p(x) be the polynomial p(x) = x" + a, x"-1 + + ajx + ao %3D The companion matrix of p(x) is the n X n matrix an-1 -an-2 - ao 1 C(p) = 1 (4) 1 (a) Show that the companion matrix C(p) of p (x) = x' + ax + bx + c has characteristic polynomial -(A3 + al? + ba + c). (b) Show that if A is an eigenvalue of the companion %3D matrix C(p) in part (a), then A is an eigenvector of C(p) corresponding to A. 1

Q: Find the characteristic polynomial of the matrix 5 A 0 -5 -1 -4

A: Characteristic polynomial is obtained using the expression |A-λI|, where I is the identity matrix.

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Q: 星 Find a singular value decomposition of the matrix A. 港 -1 要 A = - %3D -1 星 里

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Q: Find a singular value decomposition (SVD) of the matrix: 3 2 2 H = 2 3 -2

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Q: Find the characteristic polynomial and the eigenvalues of the matrix. 6 -2 - 5 2.

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Q: Find the characteristic polynomial and the eigenvalues for the matrix 1 -1 1 -1 -1 1 -1 -1 F : -1 -1…

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Q: Find the characteristic polynomial of the matrix 1 -2 A = -1 -3 3

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Q: Find the singular value decomposition of a matrix A={ 1 1, 0 1, 1 -1 }.

A: To find - Find the singular value decomposition of a matrix

Q: (IV) There exists a matrix A with eigenvalue 5 whose algebraic multiplicity is 2 and geo- metric…

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Q: A=PDP-1

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Q: 1. Let A be an m X n real matrix with full column rank. Show that the Gram matrix AT A associated…

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 0-7 A-2 1-1 4 6 010-3 0-3-5 1.1 TRANSFORM TO…

A: A=7-340-721-146010-3-5

Q: .

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Q: prior to Exercises 15–18 in Section 3.1. [Note: Finding the characteristic polynomial of a 3 x 3…

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Q: Consider the matrix, -2 -1 -17 A = -3 0 π 0 0 3 a) Compute the characteristic polynomial and the…

A: Solving

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Q: a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. matrix A for…

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A: see attachments

Q: The characteristic polynomial of A is p(λ) = λ3−3λ2+4. Find its eigenvalues.

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Q: (b) Show that an n x n complex matrix is unitarily diagonalizable if and only if it is normal.

A: By using Schurs theorem the answer is given as follows :

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