Find the permutation matrix P so that PA can be factored into the product LU, where L is lower triangular with 1's on its diagonal and U is upper triangular for these matrices.

So the back of the book shows:

Which I tried working out and got the same answer. I didn't interchange the first and second row which I assume the book didn't either.

But MATLAB shows this:

The other one I did was and got but MATLAB shows

All the other questions, the P in the back of the book and MATLAB are the same. I noticed in MATLAB, it chooses biggest number in the first column and sets that as the first row.

So is the book wrong and am I supposed to choose the biggest number in the first column and set that as the first row before I start row reducing? But how do I know if [2 2 3 7] or [2 3 4 5] is bigger?