Question

Hi everyone, looking for some help to understand linear algebra notations. I will post the detailed question below. Thanks everyone,

Answer 1

My question is referring to the follow matrix \[\left[\begin{matrix}0 &1 & 2 & 0 & 0 & 2 \\0 & 0 & 0 & 1 & 0& 3 & \\ 0 & 0 & 0 & 0 & 1 & 4 &\\0 & 0 &0 & 0 &0 &0\end{matrix}\right]\]

Then the book states "It is useful to denote the column numbers in which the leading entries 1 occur, by c1,c2...cr,, with remaining columns being cr+1...cn where r is the number of non-zero rows. For this matrix is gives the example of r=3, c1=2, c2=4, c3=5, c4=1, c5=3, c6=6.

I dont understand this, what does it mean? How did they get all those numbers for each c?