General Matthews received his commission from the U.S. Air Force Academy, earning a bachelor of science degree in Engineering Sciences and later a master's in Operations Research from Princeton University. A career fighter pilot and a distinguished graduate of the USAF F-15 Fighter Weapons School, General Matthews commanded at the squadron, group, and wing level. He also served as Commandant of the Air Force Institute of Technology and served tours in the Pentagon for Headquarters USAF and the Joint Staff. He culminated his 34-year active-duty career as the Director, Strategy, Plans and Assessments, U.S. Forces-Iraq before joining the Raytheon Company as Vice President of USAF Programs from 2011–2018. In addition to serving as a William & Mary Adjunct Lecturer, General Matthews is a Senior Research Advisor to George Mason University's Rapid Prototyping Research Center and an independent consultant.