Suppose I've a matrix:

$\displaystyle A = \left[\begin{array}{rrrr} 1 & 3 & 1 & 3\\ 0 & 1 & 1 & 0\\ 0 & 0 & 0 & 1\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 \end{array}\right]$

Now the book i'm following says that "It is easy to see that in matrix $\displaystyle A$, the first, second and fourth column vectors are linearly independent (These columns have the leading $\displaystyle 1$'s)".

I don't understand this.

How did the author find out with simple examination that first, second and fourth column vectors are linearly independent?

And why this process works?

Is it possible for anyone to kindly explain this process?