[3 2 0] Consider the quadratic form Q(x) = x" Ax, where A = 2 2 2 0 2 1 (a) Given that vị 2 and v2 are two eigenvectors of the matrix A, find the eigenvalues corresponding to Vị and v2. (b) The third eigenvalue of A is –1. Find the corresponding eigenvector.

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A: Calculate the determinant of | B-lamda.i|

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Q: 3 an eigenvector of -4 F 2 19. Is ·- 9] -5 1? If so, find the eigenvalue. 4

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Q: 3. Compute all eigenvalues and eigenfunctions of x" + Bx = 0 given that x(2) = x(4) and x'(2) =…

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Q: 12 6 j' -3 3 the eigenvalues and eigenvectors for the coefficient matrix. dy = and A2 %3D

A: The matrix given to us is  y→'=126-33y

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Q: (VII). > Find the all eigenvalues and the corresponding eigenspace of matrix A, 2 0 0 where A=-1 1 3…

A: We need to find the eigenvalue and eigenvector for the given matrix. This can be done as follows:

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Q: - 4 3 Is v = - 2 an eigenvector of A = 2 -3 -2 ? If so, find the eigenvalue. -1 0 - 2 3.

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Q: Q.2 Use eigenvalues and eigenvectors to solve the (1 1 1) X'=2 1 -1x, i =-1,2,2 0 -1 1

A: Given - X' = 11121-10-11X , λ = -1, 2, 2 To find - Use eigenvalues and eigenvectors to solve the…

Q: (2 2 -2 If A.x = Ax, where A = 1 3 1 determine the eigenvalues of the 1 2 2 matrix A and an…

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Q: Q5: Find the eigenvector and eigenvalue for [2 0 1] B = 0 1 0 Lo 2 1. A = 13

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Q: 1) Consider the matrix 2. A = | 0 3 4 4 9. a) Calculate the eigenvalues. b) Find the eigenvector…

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Q: 2. Apply the eigenvalue method to find solve the initial value problem: (a) x = 3x, + 4x2 x = 3x, +…

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Q: -2 2 Find the eigenvalues and eigenvectors of the matrix A 0 1 3 0 -4 d1 =, 51 = and and 13 v3

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Q: -1 Let be the eigenvector corresponding to the largest eigenvalue of the matrix 1 -1 x A =0 -1 2 2…

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Q: (2 1 Q2) find eigenvalue eigenvector of A x(0,0) = (1,1)

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Q: 1 2 Q1) find eigenvalue eigenvector of A=(0 1 1/ 1 1

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Q: Is v= 1 3 an eigenvector of A = 1 6 -1 -4 ? If so, find the eigenvalue.

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Q: 3 Let v₁ = -3 and v2 = 2 be eigenvectors of the matrix A which correspond to the eigenvalues X1 1 0…

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Q: 3 0 -1 Find an eigenvector of A with eigenvalue 2, where A = 2 4 0 -1 1

A: Explanation of the answer is as follows

Q: Hw/ Find The eigenvalues ofo A= 3 -2 -2 1o -5 O A= Ans/0 2.= - , 22= 2, a3:1

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Q: d the three distinct real eigenvalues of the matrx B=-3 1 -2 6.

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Q: (2 2 -2 2 If A.x = Ax, where A = 1 3 1 determine the eigenvalues of the 1 2 2 matrix A and an…

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Q: 5.2  8  the real eigenvalues are

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Q: Hw/Find The eigenvalues ofo A= 3 I4-2 -5 10 ® A= -1 2.

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Q: The second approximation of the eigenvalue obtained by the power method applied to 0 -2 A=2 -1 1…

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Q: Assume that a real 2 x 2 matrix A has an eigenvalue of 1 = 3 + 2i with a corresponding eigenvector =…

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Q: tw/ Determine The eigenvalues and eigenvectors if 2. A %3D Ans/ 2=1,2,3 %3D > X2 = X3

A: given, A=201-14-1-120 detA-λI=201-14-1-120-λ100010001=2-λ01-14-λ-1-12-λ…

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Q: 1 0 0 Find the eigenvalues A of the mat rix 220 3 4 3

A: The eigenvalues  of a matrix A are the roots of the characteristic equation det(A-λI)=0

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Q: [11-4 For the matrix03 2 Lo0 6 an eigenvector corresponding to the eigenvalue 3 is OA [1 O B.

A: We have to solve given problem:

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Q: [2 2 3 3] 1 1 The number of distinct eigenvalues of the matrix A = is equal to 0 0 33 0 0 0 2

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Q: 11] Q4: If A. x = Ax, where A = 1 3 2 determine the eigenvalues of the matrix A and an -1 1 21…

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Q: Show v2  = [ 1  0 ]T is a corresponding “generalized eigenvector” of A

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Q: Given that the matrix A has eigenvalues A = 2 with corresponding eigenvector i = and Ag = -1 with…

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Q: (1) Find the approximate dominated eigenvalue and corresponding eigenvector by us- ing Power method…

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