Governor Deval Patrick has signed into law a bill to study the feasibility of the state hosting the 2024 Summer Olympics. The bill, sponsored by Senator Eileen Donoghue, would create a nine-member commission to analyze all aspects of hosting the games, including infrastructure, transportation, security, lodging, locations, costs, and job creation. The Lowell Democrat has said that hosting the Olympics would also give the state ‘‘an amplified international profile’’ that could boost tourism. The Massachusetts Senate and House both approved the bill before sending it to Patrick, who signed it Thursday. The bill calls on the commission to complete its report by March 2014.