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.