We don't get too much detail on Matthew, the oldest son in the Garner family. For the most part, he's talked about as being one half of the "Matthew and Mark" duo. One of the few things we do know about him is that he has always dreamed of growing up and having a hog farm. (Dream big, guy.) So when the Government forces Luke's family to sell their pigs, Matt takes it pretty hard.
Being the first-born son, Matthew takes after his father a bit. Luke notices how Matthew "is starting sport the same roll of fat around his waist that Dad had" (17.68) and after saying their final goodbyes, Luke observes "Dad and Matthew look[ing] gruff" (30.5).
Like father, like son—something Luke will never know.