I would like to solve one $ 2 times $ 2 System of the form

$$ frac {d} {d theta} T = TA, quad T (0) = Id $$

from where $ theta $ is real and $ A $ is of the form

$$ A = begin {pmatrix} 0 & frac {e ^ {- i theta}} { lambda} \ frac {1} {36} e ^ {- i theta} left (9 Lambda + 2 ( lambda-1) ^ 2 (6 cos { theta} + cos {2 theta} + 6) right) & 0 end {pmatrix}, $$

With $ lambda $ a free parameter in the **unit circle**,

I am particularly interested in numerical solutions $ theta = 2 pi $ depending on the additional parameters $ lambda $, I'm pretty new with *Mathematica*and I've tried it so far:

```
T[θ_] = {{T11[θ]T12[θ]}, {T21[θ]T22[θ]}};
ON[θ_] = {{0, E ^ (- Iθ) / λ}, {1/36 E ^ (- Iθ) (9λ + 2 (-1 + λ) ^ 2 (6 + 6 Cos[θ] + Cos[2 θ])), 0}};
sys = {T & # 39;[θ] == T[θ].ON[θ]};
```

The previous code sets the system I want to solve, and now I'm trying to solve numerically. I tried it first

```
NSol = NDSolve[{sys, T11[0] == 1, T12[0] == 0, T21[0] == 0, T22[0] == 1}, {T11[θ]T12[θ]T21[θ]T22[θ]}, {θ}, {θ, 0, 2 Pi}];
```

that gives me the output

```
NDSolve :: dupv: "Double variable θ found in NDSolve[<[<[<[<<1>>], "
```

I tried too

```
Nsol2 = ParametricNDSolve[{sys, T11[0] == 1, T12[0] == 0, T21[0] == 0, T22[0] == 1}, {T11, T12, T21, T22}, {θ, 0, 2 Pi}, {λ}];
```

what gives me as an issue $ T_ {11}, dots, T_ {22} $ as *Parametric Function*s dependent on each other and on $ lambda $,

I do not know if this is the right approach and if so, how to extract a numeric expression depending on it $ lambda $ from the last issue – all I've seen in the documentation are examples that are recorded for specific parameter values. Any help is greatly appreciated.