Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X¹(0)xo is the solution to the initial value problem x'=Ax, x(0) = xo- 060 x = 1 0 1 x, x(0) = 110 1 equals each side of the equation. x₁' = Ax₁ = x₂ = Ax₂ = X3' = AX3 = -3 X(t) = 060 (a) If X(t) = [x₁ (t) x₂ (t) x3 (t)] and A= 1 0 1 ⠀⠀⠀ 110 6e-t-3e-2t 8e³t e-2t 4e3t e-2t 4e³t -e-t -5e-t validate the following identities and write the column vector that
Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X¹(0)xo is the solution to the initial value problem x'=Ax, x(0) = xo- 060 x = 1 0 1 x, x(0) = 110 1 equals each side of the equation. x₁' = Ax₁ = x₂ = Ax₂ = X3' = AX3 = -3 X(t) = 060 (a) If X(t) = [x₁ (t) x₂ (t) x3 (t)] and A= 1 0 1 ⠀⠀⠀ 110 6e-t-3e-2t 8e³t e-2t 4e3t e-2t 4e³t -e-t -5e-t validate the following identities and write the column vector that
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 X(t) is a fundamental matrix for the given system and compute X ¹(t). Then use the result that if X(t) is a
fundamental matrix for the system x' = Ax, then x(t)= X(t)X¹(0)xo is the solution to the initial value problem
x'=Ax, x(0)=xo-
060
x = 1 0 1 x, x(0) =
110
1
equals each side of the equation.
x₁' = Ax₁ =
x₂ = Ax₂ =
X3' = Ax3 =
-3
X(t) =
060
(a) If X(t) = [X₁ (t) x₂ (t) x3 (t)] and A= 1 0 1
110
6e-t-3e-2t 8e³t
e-2t 4631
e-2t 4e3t
-e-t
-5e-t
validate the following identities and write the column vector that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21542042-44df-491d-ab79-595b0cfabe71%2Ff626a379-1f43-46d6-917f-86d81d4e774c%2F077yf8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Verify that X(t) is a fundamental matrix for the given system and compute X ¹(t). Then use the result that if X(t) is a
fundamental matrix for the system x' = Ax, then x(t)= X(t)X¹(0)xo is the solution to the initial value problem
x'=Ax, x(0)=xo-
060
x = 1 0 1 x, x(0) =
110
1
equals each side of the equation.
x₁' = Ax₁ =
x₂ = Ax₂ =
X3' = Ax3 =
-3
X(t) =
060
(a) If X(t) = [X₁ (t) x₂ (t) x3 (t)] and A= 1 0 1
110
6e-t-3e-2t 8e³t
e-2t 4631
e-2t 4e3t
-e-t
-5e-t
validate the following identities and write the column vector that
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