Efficient way to solve homogenous system with complex numbers?

51 Views Asked by At

I need to find how many solutions there are for the system:

$$\begin{bmatrix}2+i&3+i&2 \\ 1&4i&5 \\ i+3&5&2-3i\end{bmatrix}x = 0$$

I assume it can be solved using normal row operations - Gausian elimination.

But, its complex and hard with complex numbers.

Therefore the question is: Is there is another, more convenient/smart way to solve such equations?

I obviously prefer a general way and not specific to the question, if there is such.