Born in Ljubljana on 13th December 1983, his first interactions with the trumpet were through his father, also a trumpet player, who became his first teacher. Matković achieved success at an early age including three successive Slovenian State Competition wins. He first came into contact with jazz music through his father’s records. By listening to trumpet players, such as Miles Davis, Clifford Brown, Thomasz Stanko, Jon Hassell and many others, he became closer to the jazz sound he later followed.
At the Ljubljana Music Conservatory, where he currently works as Professor of Jazz Trumpet, he attended the department for classical and jazz music. He later continued his education at the University of Graz(Austria), where he completed his Master’s degree in 2009 under the mentorship of Professor Edvart Holntaner. Traveling through Europe and America -New York- he also studied with trumpet players, including Stjepko Gut, John Swana, Charles Toliver, Dave Rodgers and Erik Vloemians.

He began to associate with musicians from different music genres at an early stage in his career and took part in various projects as trumpeter, keyboard player and as producer. He has recorded over 30 albums in collaboration with different groups across a range of genres.

As a member of both small groups and big bands, he has worked alongside Stjepko Gut, Bob Brookmeyer, Johnathan Blake, Jure Pukl, Renato Chicco, Igor Bezget, RTV Big Band, European Movement Jazz Orchestra, European Youth jazz Orchestra, KUG Big Band, Fool Cool Jazz Orchestra, Robert Jukič, Jazz Club Gajo Quintet, and many others. He is a regular member of the European Movement Jazz Orchestra since 2008, with whom he released a record at well known label Clean Feed in 2011.

He has performed at many top festivals both at home and abroad. These include Cairo Jazz Festival (Egypt), Bundes Jazz Festival
(Bonn, Germany), Lent Festival (Maribor, Slovenia), 50th Ljubljana Jazz Festival (Slovenia), Cerkno Jazz festival (Slovenia), Jazz Club Porgy and Bess (Vienna, Austria), Maribor National House (Slovenia),
Brussels Goethe Institute (Belgium), Centro Cultural Vila Flor (Guimaraes, Portugal), Teatro Gil Vincente (Coimbra, Portugal), Casa da Musica (Porto, Portugal), Centro Cultural de Belem (Lisbon, Portugal)(with Maria Joao), Palais des Beaux-Arts (Brussels, Belgium), Konzerthaus (Berlin, Germany) and Rome Goethe Institute (Italy).

His music debut "Motion In Two Dimensions” – a duo with pianist Marko Črnčec – was released in 2010. The record presents their interpretations of well-known jazz standards. Critics described the album as a "…comprehensive approach… mastering the jazz tradition.”