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Consider a System of Homogeneous First-Order Linear Differential Equations of the Form

Question 28

Multiple Choice

Consider a system of homogeneous first-order linear differential equations of the form $Consider a system of homogeneous first-order linear differential equations of the form = Ax, where A is a 2 × 2 constant matrix. are solutions of this system, which of the following must also be solutions of this system? Select all that apply. A) -2 \mathbf{x}_{1}(t) B) -7.2 \mathbf{x}_{1}(t) +4.4 \mathbf{x}_{2}(t) C) \mathbf{x}_{1}(t) \cdot \mathbf{x}_{2}(t) D) -6.6 t \mathbf{x}_{1}(t) +5.8 t x_{2}(t) E) \left.\left(7.2 \mathbf{x}_{1}(t) +5.4 \mathbf{x}_{2}(t) \right) -8\left(\mathbf{x}_{1}(t) -\mathbf{x}_{2} t\right) \right) F) 2 \mathbf{x}_{1}(t) -3.6 \mathbf{x}_{2}(t) -4.6$ = Ax, where A is a 2 × 2 constant matrix. $Consider a system of homogeneous first-order linear differential equations of the form = Ax, where A is a 2 × 2 constant matrix. are solutions of this system, which of the following must also be solutions of this system? Select all that apply. A) -2 \mathbf{x}_{1}(t) B) -7.2 \mathbf{x}_{1}(t) +4.4 \mathbf{x}_{2}(t) C) \mathbf{x}_{1}(t) \cdot \mathbf{x}_{2}(t) D) -6.6 t \mathbf{x}_{1}(t) +5.8 t x_{2}(t) E) \left.\left(7.2 \mathbf{x}_{1}(t) +5.4 \mathbf{x}_{2}(t) \right) -8\left(\mathbf{x}_{1}(t) -\mathbf{x}_{2} t\right) \right) F) 2 \mathbf{x}_{1}(t) -3.6 \mathbf{x}_{2}(t) -4.6$ are solutions of this system, which of the following must also be solutions of this system? Select all that apply.

A) $-2 \mathbf{x}_{1}(t)$
B) $-7.2 \mathbf{x}_{1}(t) +4.4 \mathbf{x}_{2}(t)$
C) $\mathbf{x}_{1}(t) \cdot \mathbf{x}_{2}(t)$
D) $-6.6 t \mathbf{x}_{1}(t) +5.8 t x_{2}(t)$
E) $\left.\left(7.2 \mathbf{x}_{1}(t) +5.4 \mathbf{x}_{2}(t) \right) -8\left(\mathbf{x}_{1}(t) -\mathbf{x}_{2} t\right) \right)$
F) $2 \mathbf{x}_{1}(t) -3.6 \mathbf{x}_{2}(t) -4.6$