Homogeneous system of linear equations over $\mathbb{C}$ I have two systems of linear equations and I need to verify if they are indeed the same system, and if they are I must rewrite each equation as a linear combination of the others. A: $\begin{array}{cc} 2x_1 + (-1+i)x_2 +x_4 = 0 \\ 3x_2 -2ix_3+5x_4=0\end{array}$
B: $\begin{array}{cc} (1+i/2)x_1 +8x_2 -ix_3 -x_4=0 \\ \frac{2}{3}x_1 -\frac{1}{2}x_2 + x_3 +7x_4=0 \end{array}$
My confusion lies in the fact that when I solve for $x_1,x_3$ in system A, I can get solutions in terms of $x_2,x_4$, whereas if I solve for $x_1,x_3$ in system B, $x_1$ is a function of $x_3$ and vice versa. This leads me to believe that the systems are not the same, but when I try and solve this system using mathematica, I am told that only trivial solution exists for both systems. 
I was able to do this for the simpler examples with real variables but this one has me stumped.
Please note : this is the very beginning of my course so please refrain from using more advanced linear algebra techniques.
Thanks for the help!
A: In B, multiply 2nd equation by $i$, add to 1st equation (so $x_3$ disappears), solve for $x_1$ in terms of $x_2$ and $x_4$, substitute this into either original equation of B, solve for $x_3$ in terms of $x_2$ and $x_4$, compare with your answer for A. 
