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Verify that the vector functions x₁ = 2-1 - [3 =2)x 0² (-00 3-2 is a particular solution to the nonhomogeneous system x'=Ax + f(t), where f(t)=4col (e¹.t). Find a that xp 6 general solution to x'=Ax+ f(t). and X₂ ---4-8- -2e" -bet are solutions to the homogeneous system x'=Ax= (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. =Ax₁- x₁' x₂ = AX₂= (-00,00), and

Verify that the vector functions x₁ = 2-1 - [3 =2)x 0² (-00 3-2 is a particular solution to the nonhomogeneous system x'=Ax + f(t), where f(t)=4col (e¹.t). Find a that xp 6 general solution to x'=Ax+ f(t). and X₂ ---4-8- -2e" -bet are solutions to the homogeneous system x'=Ax= (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. =Ax₁- x₁' x₂ = AX₂= (-00,00), and

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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Verify that the vector functions x₁ = that xp=6 te general solution to x'=Ax+ f(t). and X₂ -6e-t are solutions to the homogeneous system x' = Ax= 3-2 (-00,00), and is a particular solution to the nonhomogeneous system x' = Ax+ f(t), where f(t)=4col (e¹.t). Find a (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. x₁ =Ax₁ x₂ = AX₂
Transcribed Image Text:Verify that the vector functions x₁ = that xp=6 te general solution to x'=Ax+ f(t). and X₂ -6e-t are solutions to the homogeneous system x' = Ax= 3-2 (-00,00), and is a particular solution to the nonhomogeneous system x' = Ax+ f(t), where f(t)=4col (e¹.t). Find a (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. x₁ =Ax₁ x₂ = AX₂
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