April Long Fault Tolerance editorial explanation?

I didn’t get the gaussian elimination method. Here servers and chunks are denoted along rows and columns respectively, then to convert 1 into 0 they Xor two columns. But isn’t it conceptually wrong to Xor 2 different chunks? Remember that column operations are invalid in Gauss Elimination for solving linear equation.

Here they have assumed servers to be the linear combinations of chunks, which may have 1 or 0 as coefficient, But isn’t it chunks which are linear combinations of servers?

Kindly post your question on the editorial page of Fault Tolerance here: discuss.codechef.com/questions/8121/fault-editorial