Maj. Gen. Jeff Burton, the Guard adjutant general, called Matthews "not only a great state figure but also a national figure."
"He was a great leader, friend and mentor to many. There are a lot of wet eyes today because of his loss," Burton said, according the release.
In an interview with The Salt Lake Tribune at the end of his 40-year military career, Matthews, a Sandy resident, said his greatest challenges had been the floods of 1983 and Desert Storm, the 1990 invasion of Iraq by U.S. and coalition forces.
Matthews' career high point was serving as president of the National Guard Association, he said at the time.
An educator in his civilian life, Matthews served as principal of Dixon Junior High School in Provo and later as the first principal at Timpview High School, also in Provo.
Matthews was commissioned a second lieutenant through the BYU Air Force ROTC program in December 1954. After receiving his pilot's wings, he was an instructor pilot on active duty and joined the Utah Air Guard as a fighter-interceptor pilot in 1959.
He was named air commander of the Utah Air National Guard in 1979 after serving as commander of the 151st Air Refueling Group. He flew missions accumulating 7,300 miles, including airlifts in and out of Vietnam, the last of which was in 1972.
Matthews was first appointed Utah adjutant general in 1982, by then-Gov. Scott Matheson. He was the first Air National Guard officer to hold the position. He was reappointed by then-Gov. Norm Bangerter in 1988.
Maj. Gen. James M. Miller replaced Matthews, who went on to serve as a military adviser to Gov. Mike Leavitt.
Burton said Matthews was a gentleman who set a tone of professionalism in the Guard.
"His style was one of mentorship," Burton said, according to the news release. "He led in a kind way; it was leadership by inspiration and not by fear. He connected with all people at all levels."
Funeral details had not been announced by late Tuesday. The Guard will provide full military honors, the release said.