Defective matrix System of ODE - algebraic multiplicity 2 and geometric multiplicity 1

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First order linear system of differential equations
In this example the matrix has an algebraic multiplicity of 2, but having only a geometric multiplicity of 1. (Defective matrix)

Algebraic multiplicity of 2 = we have 2 eigen values (repeating)
Geometric multiplicity of 1 = we have 1 linearly independent eigen vector
( A second generalized eigen vector needs to be found)

Advanced differential equations
Link to another similar, but more complicated example:
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