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The state transition matrix Φ(t) of a system [ẋ1; ẋ2] = [[0, 1], [0, 0]] [x1; x2] is

1. [[t, 1], [1, 0]]
2. [[1, 0], [t, 1]]
3. [[0, 1], [1, t]]
4. [[1, t], [0, 1]]

Correct answer: [[1, t], [0, 1]]

Solution

The state transition matrix Φ(t) describes how the state of a linear system evolves over time. For the given system, the correct matrix [[1, t], [0, 1]] reflects the solution to the system's differential equations, indicating that the first state remains constant while the second state evolves linearly with time.

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