P3.19 Consider the system described by 0 1 * (t) = [º₁__¹4 ] × (t), x -4 where x(t) = (x₁ (t), x₂ (t))T. (a) Compute the state transition matrix Þ(t,0). (b) Using the state transition matrix from (a) and for the initial conditions £₁ (0) = 1 and x₂ (0) = −1, find the solution x(t) for t> 0.

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P3.19 Consider the system described by
0
* (t) = [ ₁ 14]x (t),
where x(t) = (x₁ (t), x2 (t))¹. (a) Compute the state transition matrix
Þ(t,0). (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.
Transcribed Image Text:P3.19 Consider the system described by 0 * (t) = [ ₁ 14]x (t), where x(t) = (x₁ (t), x2 (t))¹. (a) Compute the state transition matrix Þ(t,0). (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.
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