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10. LINEAR DIFFERENTIAL SYSTEMS

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10. LINEAR DIFFERENTIAL SYSTEMS

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This means that the familiar elimination method, used for solving algebraic systems like

can be adapted to solve any system of linear differential equations with constant coefficients. Our goal in this section is to formalize this elimination method so that we can tackle more general linear constant coefficient systems.

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If it turns out that

is the zero operator, the system is said to be degenerate.

As with the anomalous problem of solving for the points of intersection

of two parallel or coincident lines, a degenerate system may have no

solutions, or if it does possess solutions, they may involve any number

of arbitrary constants

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