Question

Write the given linear system in matrix form. Assume X = x y z . dx dt = −3x + 6y − 9z dy dt = 7x − y dz dt = 10x + 6y + 3z

Answer 1

Answer:

Step-by-step explanation:

Consider the system:

$\begin {Bmatrix} \dfrac{dx}{dt}=-3x+6y-9z \\ \\ \dfrac{dy}{dt}=7x -y \\ \\ \dfrac{dz}{dt}= 10 x + 6y + 3z\end {Bmatrix}$

The matrix form of the system is:

$\begin {bmatrix} \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix} = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right]$

Which can be written as:

$X' = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] X$

where;

$X' = \begin {bmatrix} \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix} \ \ \ \& \ \ \ X = \left[\begin{array}{c}x\\y\\z\end{array}\right]$