I want to solve equations analytically and found my equation can be composed as Hermitian matrix. So I found on MMA that there is a Cholesky method that I can use to solve this matrix. However, since it is not the numerical solution, I am having little trouble solving my equations. Here is the simple example what I am struggling with

LinearSolve[{{a, b}, {Conjugate[b], c}}, {d, e}, Method -> "Cholesky"]

LinearSolve::herm: The matrix {{a,b},{Conjugate[b],c}} is not 
Hermitian or real and symmetric.

If I do not use the methods, then I will get the answer.

LinearSolve[{{a, b}, {Conjugate[b], c}}, {d, e}, Method -> "Cholesky"]

$\left\{\frac{c d-b e}{a c-b b^*},\frac{a e-d b^*}{a c-b b^*}\right\}$

However, I want to use the method to boost speed of my calculation. Do you have any suggestion?