Answer:
Step-by-step explanation:
Consider the system:
[tex]\begin {Bmatrix} \dfrac{dx}{dt}=-3x+6y-9z \\ \\ \dfrac{dy}{dt}=7x -y \\ \\ \dfrac{dz}{dt}= 10 x + 6y + 3z\end {Bmatrix}[/tex]
The matrix form of the system is:
[tex]\begin {bmatrix} \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix} = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
Which can be written as:
[tex]X' = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] X[/tex]
where;
[tex]X' = \begin {bmatrix} \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix} \ \ \ \& \ \ \ X = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
