Consider this system of ODEs- x'=-2x+2y, y'=8x-2y, x=x(a), y=y(a) A) Set up a matrix B and write the system in the form x'=Bx, find the eigenvalues of B B) Determine the eigenvector for each eigenvalue C) find the general solution

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Q: FIND THE FUNDAMENTAL MATRIX AS WELL AS THE FUND AMENTAR MATRIX ø (6)= I %3D SATISEYING x' = 2 -5 -2

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Q: Find the eigenvalues and eigenfactor for the two by two matrix [0,1;-2,1]

A: Step 1:Step 2: Step 3:

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Q: For the linear system j' Find the eigenvalues and eigenvectors for the coefficient matrix. , 01 = ,…

A: See solution below

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Q: For the linear system Find the eigenvalues and eigenvectors for the coefficient matrix. = --[-¹0…

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Q: (d) cation. [11] =2 Write out eigendecomposition of A and verify it with the matrix multipli- m,

A: Eigenvalue decomposition:A=QDQ−1Where the columns of Q are the orthonormal eigenvectors and the…

Q: x'=-13x-8y-4z, y'=12x+7y+4z, z'=24x+16y+7z, where x=x(a), y=y(a), z=z(a) A) Write out the matrix B…

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Q: O A₁2, V₁ = = O A₁2, V₁ = = O A₁-2, V₁ = = The phase portrait shown above is for a linear system…

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Q: The set of eigenvalues of the matrix A=[2 0 -1; 6 8 -5; 9 9 -7]∈ R^3x3is equal to: (a) {1,2}, (b)…

A: Step 1: The provided matrix is:A=⎣⎢⎡​269​089​−1−5−7​⎦⎥⎤​∈R3×3   .........(1)It is needed to…

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

Q: For the system of differential equations, = A₁, A₂ = U₁ = U2 = y' a) Find the characteristic…

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Q: How and why are eigenvectors used to describe solution sets of linear systems of ODE's?

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Q: Let -1 B := 1 (a) Find the eigenvalues and eigenvectors of B (b) Use your answers in part (a) to…

A: The given matrix is,

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Q: y₁' = 5y₁ + 3y2 Y2' = -6y₁4y2

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Q: a) Find the eigenvalues of A. b) Find three linearly independent solutions of x' = Ax. c) Find the…

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