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Consider a system of homogenous first-order linear differential equations of the form x'- Ax, where A is a 2 x 2 constant matrix. If X₁ (1)= and x₂ (1)= are solutions of this system, which of the following must also be solutions of the system? Select all that apply. 4.5x, (f) □x, (1) - N₂ (1) D-5.6x: (1)+7.2%, (1) D-6.2rx (1)+5.4rx; (f) E-SAND +S45 □ (2.4x, () +2.8x: ())-2(x, ()-x; (0))

Consider a system of homogenous first-order linear differential equations of the form x'- Ax, where A is a 2 x 2 constant matrix. If X₁ (1)= and x₂ (1)= are solutions of this system, which of the following must also be solutions of the system? Select all that apply. 4.5x, (f) □x, (1) - N₂ (1) D-5.6x: (1)+7.2%, (1) D-6.2rx (1)+5.4rx; (f) E-SAND +S45 □ (2.4x, () +2.8x: ())-2(x, ()-x; (0))

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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Consider a system of homogenous first-order linear differential equations of the form x'= Ax where A is a 2 x 2 constant matrix, If Se' X1 (1) = and x₂ (1) = are solutions of this system, which of the following must also be solutions of the system? Select all that apply. 4.5x, (f) □xy (1)-X₂ (1) -5.6x2 (1)+7.2x, (1) D-6.21x, (1)+5.41x₂ (1) 0 -54x(0)+5+5 □ (2.4x, (f) + 2.8x: ())-2(x, (1)-x; (1))
Transcribed Image Text:Consider a system of homogenous first-order linear differential equations of the form x'= Ax where A is a 2 x 2 constant matrix, If Se' X1 (1) = and x₂ (1) = are solutions of this system, which of the following must also be solutions of the system? Select all that apply. 4.5x, (f) □xy (1)-X₂ (1) -5.6x2 (1)+7.2x, (1) D-6.21x, (1)+5.41x₂ (1) 0 -54x(0)+5+5 □ (2.4x, (f) + 2.8x: ())-2(x, (1)-x; (1))
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