The Matterhorn (14,690') is certainly one of the most iconic summits on Earth. It is also a difficult climb, with no easy route to the summit. Ian Corless puts it this way:
"...the Matterhorn is a mountain on the border between Switzerland and Italy. At 4,478 meters (14,690 ft) high, it one of the highest peaks in the Alps. It consists of four steep faces, striking above the glaciers that surround it. Overlooking the town of Zermatt it is an iconic mountain and possibly ‘the’ most photographed mountain in the world. It is a mountain that dreams are made of. Kilian Jornet is no different, 'I have been dreaming about this record since I was 15'."
Despite its difficulty and dangers, the Matterhorn is climbed by thousands every year. The least difficult and by far most popular route is the Hörnli Ridge. The Lion Ridge ascends from Brueil-Cervinia on the Italian side of the mountain, and is the shortest route. It has many fixed ropes in place. This is the route taken by both Brunod in his 1995 record, and by Jornet in 2013. Jornet attempted the record as part of his Summits of my Life project. Salomon has produced some slick videos of Jornet's exploits, including this and this, which include interviews with Brunod and neat archival footage of his 1995 run. Ian Corless has an excellent interview with Jornet done shortly after his successful record run, which also includes more information on the mountain and routes, Brunod, and the record.
Because these athletes used fixed ropes we consider these ascents "supported".