Suppose x(t) is the solution of the following initial value problem in ℝ2
ẋ = Ax, x(0) = x0, where A = \(\left[\begin{array}{ll}5 & 4 \\1 & 2\end{array}\right]\).
Which of the following statements is true?
1
x(t) is a bounded solution for some x0 ≠ 0.
2
e−6t|x(t)| → 0 as t → ∞, for all x0 ≠ 0.
3
e−t|x(t)| → ∞ as t → ∞, for all x0 ≠ 0.
4
e−10t|x(t)| → 0 as t → ∞, for all x0 ≠ 0.