Problem 4. (20 points) Consider a LTV system (t) = A(t)x(t) where x(t) = R² and === 3 A(t) == -2-6t 4+8t] -1-2t 2+2t -2 4 = +2t. -1 2 A1 A2 Vt ≥ 0. ' Note that A₁ is the exact same state dynamics matrix in Problem 3 (hence A² = 0) and A₂ = A₁-I. Find the fundamental matrix (t), namely, the state transition matrix (t,0), of the system.

FINANCIAL ACCOUNTING
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ISBN:9781259964947
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Chapter1: Financial Statements And Business Decisions
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Problem 4. (20 points) Consider a LTV system (t) = A(t)x(t) where x(t) = R² and
===
3
A(t) ==
-2-6t 4+8t]
-1-2t 2+2t
-2 4
=
+2t.
-1 2
A1
A2
Vt ≥ 0.
'
Note that A₁ is the exact same state dynamics matrix in Problem 3 (hence A² = 0) and A₂ = A₁-I.
Find the fundamental matrix (t), namely, the state transition matrix (t,0), of the system.
Transcribed Image Text:Problem 4. (20 points) Consider a LTV system (t) = A(t)x(t) where x(t) = R² and === 3 A(t) == -2-6t 4+8t] -1-2t 2+2t -2 4 = +2t. -1 2 A1 A2 Vt ≥ 0. ' Note that A₁ is the exact same state dynamics matrix in Problem 3 (hence A² = 0) and A₂ = A₁-I. Find the fundamental matrix (t), namely, the state transition matrix (t,0), of the system.
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