Consider the linear system y​′=Ay​ with
A=[3 1 0]
[0 3 2]
[0 0 5]
The eigenvalues are λ1 =3 with multiplicity 2 and λ3=5. There is one eigenvector
v1=[1]
[0]
[0]
for λ1​=3. For λ3​=5, and eigen vector is
v2​=[1]
[2]
[2]
Find a second generalized vector for λ1​ and write the general solution to the linear system.