When police arrived at the apartment complex in South Los Angeles, Dixon was standing on a second-floor balcony waving a handgun and telling officers to shoot her, police said.
She shouted "I've wasted my life," neighbors told the Los Angeles Times.
Officers ordered her numerous time to drop the gun, but she refused. At one point she climbed onto the balcony rail and stood on it, as if preparing to jump, police said.
When she eventually put the gun down on the balcony floor, officers quickly tackled and arrested her, police said.
The 5-year-old was declared dead at the scene, Eisenman said. The younger boy was shot multiple times and remained in critical condition at Cedars-Sinai Medical Center on Saturday night.
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