please help, why 19 century economy remain agricultural and the northern diversified?

Answer 1

I assume you mean the US south vs north.
The climate in the south is hot much of the year so until air conditioning became common, work that could be done in cooler climates was not done in the south.
Transportation was mostly by water, and the south does not have a river system that works well for transport except along the Mississippi.
The economy in the south dependent on slave labor, so offered few opportunities for emigrant to work and become successful, so most settled in the north.