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

Explanation:

Consider the system:

`\begin {Bmatrix} (dx)/(dt)=-3x+6y-9z \\ \\ (dy)/(dt)=7x -y \\ \\ (dz)/(dt)= 10 x + 6y + 3z\end {Bmatrix}`

The matrix form of the system is:

`\begin {bmatrix} (dx)/(dt) \\ \\ (dy)/(dt) \\ \\ (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} (dx)/(dt) \\ \\ (dy)/(dt) \\ \\ (dz)/(dt)\end {bmatrix} \ \ \ \& \ \ \ X = \left[\begin{array}{c}x\\y\\z\end{array}\right]`