Consider the first-order homogeneous system of linear differential equations
$Consider the first-order homogeneous system of linear differential equations Which of these is the general solution of the system? Here, C1 and C2 are arbitrary real constants. A) \mathbf{x}(t) =C_{1}\left(\begin{array}{c}-1 \\ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}-1 \\ 1\end{array}\right) B) x(t) =C_{1}\left(\begin{array}{c}-1 \\ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}1 \\ -1\end{array}\right) C) \mathbf{x}(t) =C_{1}\left(\begin{array}{l}1 \\ 0\end{array}\right) e^{2 t}+C_{2}\left(\begin{array}{c}-1 \\ 1\end{array}\right) D) \mathbf{x}(t) =C_{1}\left(\begin{array}{l}0 \\ 1\end{array}\right) e^{2 t}+C_{2}\left(\begin{array}{l}1 \\ -1\end{array}\right)$
Which of these is the general solution of the system? Here, C₁ and C₂ are arbitrary real constants.

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The Answer of Consider the first-order homogeneous system of linear differential equations Which of these is the general solution of the system? Here, C₁ and C₂ are arbitrary real constants. A) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{c}-1 \ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}-1 \ 1\end{array}\right) $ B) $ x(t)=C_{1}\left(\begin{array}{c}-1 \ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}1 \ -1\end{array}\right) $ C) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}1 \ 0\end{array}\right) e^{2 t}+C_{2}\left(\begin{array}{c}-1 \ 1\end{array}\right) $ D) $ \mathbf{x}(t)=C_{1}\left(\begin{array}{l}0 \ 1\end{array}\right) e^{2 t}+C_{2}\left(\begin{array}{l}1 \ -1\end{array}\right) $

Consider the First-Order Homogeneous System of Linear Differential Equations x(t)=C1(−10)e−2t+C2(−11) \mathbf{x}(t)=C_{1}\left(\begin{array}{c}-1 \\ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}-1 \\ 1\end{array}\right) x(t)=C1​(−10​)e−2t+C2​(−11​)

Consider the First-Order Homogeneous System of Linear Differential Equations
$\mathbf{x}(t)=C_{1}\left(\begin{array}{c}-1 \\ 0\end{array}\right) e^{-2 t}+C_{2}\left(\begin{array}{c}-1 \\ 1\end{array}\right)$