In[]:=
M=
-2κ
0
0
Γ2
-

Γ2


Γ1
-Γ1
0
0
0
0
-2
ω
c
-2κ
0
-2Γ1
0
-2

Γ2
0
0
0
0
0
0
2
ω
c
-2κ
0
2

Γ1
0
2Γ2
0
0
0
-

Γ2
-

Γ1
0
-κ-(
ω
c
+
ω
a
)
0
-2Γ3
0
-Γ1
0
-

Γ2
-Γ2
0
Γ1
0
-κ+(
ω
c
+
ω
a
)
0
2

Γ3
0


Γ1
Γ2
-Γ1
Γ2
0
2

Γ3
0
-κ+(
ω
c
-
ω
a
)
0
0
-

Γ2
-Γ1
-

Γ1
0
-

Γ2
0
0
-κ
0
Γ2
0


Γ1
0
0
0
-2

Γ1
0
0
-2

Γ2
-2
ω
a
0
-2Γ3
0
0
0
0
2Γ1
2Γ2
0
0
2
ω
a
2

Γ3
0
0
0
Γ2
-

Γ2
-

Γ1
Γ1
2

Γ3
-2Γ3
0
;​​b=
0
0
0


Γ2
-Γ2
0
0
2Γ3
-2

Γ3
0
;
In[]:=
$Assumptions={κ∈PositiveReals,
ω
c
∈PositiveReals,
ω
a
∈PositiveReals};
vector=LinearSolve[M,b];​​vector[[1]]
Out[]=
$Aborted
In[]:=
Inverse[M].b//FullSimplify
Out[]=
$Aborted