Consider the system of differential equations y = Ay where A is a 2 2 matrix.

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Consider the system of differential equations y′ = Ay where A is a 2 × 2 matrix. For what values of a11, a12, a21, a22 do the component solutions y1(t), y2(t) tend to zero as t → ∞? In particular, what must be true about the determinant and the trace of A for this to happen?
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