Question

The matrix form of the linear system $\frac{dx}{dt}=3x-5y$ and $\frac{dy}{dt}=4x+8y$

• A. $\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}3& -5\\ 4& 8\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$
• B. $\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}3& 8\\ 4& -5\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$
• C. $\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}4& -5\\ 3& 8\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$
• D. $\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}4& 8\\ 3& -5\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$

Answer 1

The correct option is A $\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}3& -5\\ 4& 8\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$

$\frac{dx}{dt}=3x-5y$
$\frac{dy}{dt}=4x+8y$
matrix form is:
$\frac{d}{dt}\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left[\begin{array}{cc}3& -5\\ 4& 8\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}$
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