Defective matrix System of ODE - algebraic multiplicity 3 while geometric multiplicity of 2

First order linear system of differential equations
In this example the matrix has an algebraic multiplicity of 3, but having only a geometric multiplicity of 2. (Defective matrix)

Algebraic multiplicity of 3 = we have 3 eigen values
Geometric multiplicity of 2 = we have 2 linearly independent eigen vectors
( A third generalized eigen vector needs to be found)

Advanced differential equations