The Nissan truck was driving fast at the time of the collision, police say, and it ended up crashing into an apartment building after hitting the two pedestrians.
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Police say the pedestrians were a mother walking with her first-grade daughter to school at nearby Hancock Elementary.
"From what we got from witnesses, they just described pure chaos, as the truck struck the apartment building," said Bruce Borihan, spokesman for the Los Angeles Police Department. "Officers were pretty quick to respond and took that driver into custody and transported him to a local hospital."
The driver of the truck, a 30-year-old man, was injured and transported to a hospital in stable condition. The 6-year-old girl was transported in critical condition.
The crash occurred shortly before 8 a.m. in the 6200 block of West Colgate Avenue.
The woman was pronounced dead at the scene, fire officials said. She was not immediately identified.
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Video from AIR7 HD showed the truck, with its front end mangled, sitting on a grassy area just outside the two-story apartment building.
The cause of the collision is under investigation.
Police say they have many witnesses to interview as there were other parents walking their children to school at the time.