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.
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. 
