Ismaaiyl Brinsley, who had drifted between friends and family members for most of his short life, alienating most of them and failing at almost anything that he tried, decided to come home on Saturday. He boarded a bus in Baltimore, arrived in Midtown Manhattan just before 11 a.m., and then disappeared onto the N train at the Times Square subway stop.

He was bound for Brooklyn, where he had been born 28 years before, carrying the silver Taurus 9-millimeter pistol he had used earlier to shoot his ex-girlfriend.

He had a plan, which he soon shared with the world via Instagram: He wanted to kill two police officers.

By this year, Mr. Brinsley had become isolated. He was estranged from his family. His on-again, off-again relationship with Shaneka Thompson, 29, who works for the Maryland Department of Welfare and serves in the Air Force Reserve, was off again. By Saturday, he had seized on the deaths at the hands of police officers of Eric Garner on Staten Island and Michael Brown in Ferguson, Mo., focusing his rage against the authorities. In his short life, during which Mr. Brinsley failed to finish high school, to hold a steady job or, seemingly, to commit even the smallest crime without being caught, thoughts of revenge seemed to be the one thing giving him purpose, the New York Times reports.