Matt Barnes promised last month he would exercise his $1.9 million option for 2011-12 and remain with the Lakers, and he and the team made it official today. Barnes, a backup small forward, averaged 6.7 points, 4.3 rebounds and 1.3 assists in 19.2 minutes over 53 games after signing as a free agent last July 22. He was just starting to make an impact when he injured his right knee and had to undergo surgery at midseason. He sat out 28 games. it will be interesting to see how he fares in coach Mike Brown’s new offense. Barnes was the only Lakers player to attend Brown’s introductory press conference last month.