The point of the expedition

 In 1806,  just before Luis and Clark returned, Jefferson sent Lt. Zebulon Pike with a company of soldiers to chart that southern boundary of the purchase by following the Arkansas River to its' source. Once there, he was to head south and locate the headwaters (beginning) of the Red River, then follow that river back to Louisiana.  The expedition was also given the task of escorting 51 Osage Indians back to their homes in Kansas. On top of all this, Pike was asked to continue mapping the geography, recording indigenous plants and animals, and trying to establish peaceful trade relationships with the Native Americans like Luis and Clark had done with the northern part of the Louisiana Territory.