Donīt worry. Your calculations are correct and so is the book.

where and

Factorising to is simple if you only use BO1+, which means subtracting a multiple of a row from a latter one. Sometimes you will not get by simply using BO1+. You might need to switch rows in the process, by (BO2). Now you can do this two ways, either by using a permutation matrix or by just switching the rows first as if they were like that in the beginning. It seems that this is just what matlab did since it started out with which bothers me. I donīt know how you made your calculations but I always write down the basic operation steps. It took me only one row change whereas matlab seemed to do it twice.