5. P3.19 of Dorf and BishopConsider the system described by10-[23]-2 -3x(t) =x(t)where_x(t)=(x₁(t)x₂ (t))ª .(a) Compute the state transition matrix (t).(b) Using the state transition matrix from (a) and for the initialconditions x₁(0)=1 and x₂(0)=-1, find the solution x(t) for t≥0.

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Answered: Consider the system described by 0…

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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Verify that X(t) is a fundamental matrix for the given system and compute X1(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t) = x(t)X(0)x is the solution to the initial value problem x' = Ax, x(0) = x0 - 24e-1 -9e-21 060 -5 x'= 10 1x, x(0)= 8e3t x(t)= 1 1 0 -4e-t 3e-21 3t 4e -2 -20e-t 3e-21 3t 4e 060 (a) If x(t) = [×₁ (t) x2(t) ×3(t)] and A = 10 1 validate the following identities and write the column vector that equals each side of the equation. 1 1 0 ×₁' = Ax₁ = x2' = Ax₂ = x3' = Ax3 (b) Next, compute the Wronskian of X(t). W[x()()()]= Since the Wronskian is never and each column of X(t) is a solution to x' = Ax, x(t) is a fundamental matrix. (c) Find x(t) = ☐ (d) x(t) = x(t)x¯1 (0)x₁ =
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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
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Consider the system described by 0 -=[-2₁2 x(t) = -2 -3 x(t) where x(t)=(x₁ (1)x₂ (t))". (a) Compute the state transition matrix Þ(t). (b) Using the state transition matrix from (a) and for the initial conditions x₁(0)=1 and x₂(0)=-1, find the solution x(t) for t≥0.