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Please answer question b or c. Ignore question a.

1. (30 points) Solve the given initial value problem \[ \boldsymbol{x}^{\prime}=\mathbf{A} \boldsymbol{x}, \quad \boldsymbol{x}(0)=\left(\begin{array}{lll} x_{01} & x_{02} & \ldots \end{array}\right)^{T} \] and describe the behavior of the solution as \( t \rightarrow \infty \) : (a) \( a_{11}=5, a_{12}=-1, a_{21}=3, a_{22}=1, x_{01}=2, x_{02}=-1 \). (b) \( a_{11}=-2, a_{12}=1, a_{21}=-5, a_{22}=4, x_{01}=1, x_{02}=3 \). (c) \( a_{11}=0, a_{12}=0, a_{13}=-1, a_{21}=2, a_{22}=0, a_{23}=0, a_{31}=-1, a_{32}=2, a_{33}=4 \) \( x_{01}=7, x_{02}=5, x_{03}=5 \)

Given x?=Ax, x(0)=(x01x02…)T and describe the behavior of the solution as t??. The aim is to find (b) a11=?2, a12=1, a21=?5, a22=4, x01=1, x02=3 (c) a