Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -1 -2 -2 1-4 2-4 4 and find the solution that satisfies the initial condition: Hint: 6 is an eigenvalue. a) Ox(t)= b) Ox(t)= c) Ox(t)= d) Ox(t)= 27 20 2 -2t -2 -2 27 -2t 10 20 27 -2: 3 1 -2 3 -2 -4t 1 8 42 2 -2 2 2 2 -1 1 2 1 + 27 20 3 6t 10 2 67 2 1 1 2 -3 +-H÷-344 -2 -~~ 1 2 2 A = 2 -3 HE x(0) = -2 نه به -2

Q: Consider the linear system 2 A₁ = Find the eigenvalues and eigenvectors for the coefficient matrix.…

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Q: 1. For the matrix A = 0 2 -2 3 0 1 1 2 -1 a.) Find all eigenvalues of the matrix. b.) Find all…

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Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

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Q: Give an example of an m x n matrix A such that the nonzero eigenvalues of A'A are distinct from…

A: We have to solve given problem:

Q: 7. Find the eigenvalues and eigenvectors of the following linear systems: a) b) 2x1 + 3x2= x1 4x1 +…

A: a) 2x1+3x2= λx1    4x1+3x2= λx2b)  3x1+x2 = λx1      -5x1-3x2= λx2

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A: Let A be the given 2x2 matrix                                                      A=100-1 Given…

Q: - find the eigenvectors of the diagonal matrix (Â) J where. 2 5 0-12 2 4 10 A = and P=["} 1 2 5 4 O…

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Q: Consider the following matrix: A = 3000 0 3 0-5 0 -12 -3 12 000-2 a) Find the distinct eigenvalues…

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Q: 6 Let b₁=[2] b₂ = 3 4 [ C₁ = [ ² ] ² ₂ = 1²²] > V = [] (2 13 2 and C = { C₁₂ (₂} Find and consider…

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Q: True or False? Justify your answer. d) If A is a 5×6 matrix of rank 3, then the solutions of Ax=0…

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Q: Please write clearly and without AI. Thank you

A: a.) Determining the value of the element 'a' for which the matrix A is not full-rank:  - The matrix…

Q: Consider the matrix A = /a11 0 0 a21 a22 0 a31 a32 a334 What is tr(AA')? ] Show that |A| = [1 aii.…

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Q: Consider the difference equation with initial condition Xo = That is, write xo = c1v1 + c2V2 In…

A: Here we have given a matrix M of order 2 with its eigenvalue and eigenfunctions.

Q: Consider the matrix A = /a11 0 0 a21 a22 0 a31 a32 a33 What is tr(AA')? ] Show that |A| = [1 aii.…

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Q: 2 1 -1 -1 4 -1 1 2 = 1 -1 0 -1 1 -1 0 -1 1 300 0 -1 -1 020 -1 −1 −1 003 -1 -1 0

A: if a matrix A is diagonalized it can be written as  A=PDP-1 where D is the diagonal matrix formed by…

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Q: Let M be a 3 x3 matrix with eigenvalues ₁ = -2, A2 = 0.25 A3 = 1.6 with corresponding eigenvectors 0…

A: c1=-5, c2=-14,c3=-4Explanation:Step 1: Step 2: Step 3: Step 4:

Q: 6 9 12 15 The matrix M = a b 2. , where a = 14, b = 3.9, c = -2.9, and d = 3, has two distinct real…

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