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Find a general solution to the system below. 8 -6 6 -4 x' (t) = x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x₁ (t). Then, to obtain a second linearly independent solution, try x₂(t) = te "u₁ + eu₂, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-rI)u₂ = u, to find the vector u₂. KIXE x(t) = (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)

Find a general solution to the system below. 8 -6 6 -4 x' (t) = x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x₁ (t). Then, to obtain a second linearly independent solution, try x₂(t) = te "u₁ + eu₂, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-rI)u₂ = u, to find the vector u₂. KIXE x(t) = (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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bok Find a general solution to the system below. x' (t) = 8 -6 6-4 x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x₁ (t). Then, to obtain a second linearly independent solution, try x₂(t) = te "u₁ + eu₂, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-rI)u₂ = u₁ to find the vector u₂. x(t) = (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.) Ask my instructor 20 F3 F6 ➤II ►► F9 Clear all F10 4) Show work F11 Check answer
Transcribed Image Text:bok Find a general solution to the system below. x' (t) = 8 -6 6-4 x(t) This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x₁ (t). Then, to obtain a second linearly independent solution, try x₂(t) = te "u₁ + eu₂, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A-rI)u₂ = u₁ to find the vector u₂. x(t) = (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.) Ask my instructor 20 F3 F6 ➤II ►► F9 Clear all F10 4) Show work F11 Check answer
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