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 $

Question

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 $

Quizplus · Accepted Answer

The Answer of 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 $

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