Final answer:
Thomas Jefferson had the vision of a grid system for land division following the Louisiana Purchase to ensure its efficient use and sale. This system supported his agrarian republic ideals and the westward expansion of the United States. The landmark purchase was vital for trade and the addition of farmable land, doubling the size of the nation.
Step-by-step explanation:
Thomas Jefferson had the idea to make land purchased in a grid system so all land was being efficiently utilized and sold. This approach can be traced back to the Land Ordinance of 1785, which called for the land to be divided into rectangular plots for government sale. The motive behind this was to facilitate the settlement of the frontier, making it easier for homesteaders to buy and improve the land. Moreover, Jefferson, with his vision of an agrarian republic, wanted to support trade and provide farmable land following the Louisiana Purchase, through which the United States doubled in size for the price of $15 million, an exemplary real estate deal. This territory expansion and the grid system of land division were crucial to Jefferson's agrarian ideals and the promotion of yeoman farmers which he saw as vital to the republic's success.
Furthermore, Jefferson's acquisition of the Louisiana Territory was pivotal not only for the westward expansion of the country but also for securing American control over crucial trade routes such as the Mississippi River and New Orleans. While questions of Constitutional power arose from the Purchase, Jefferson deemed the acquisition essential for the nation's development and for realizing his dream of an agrarian society based on the liberty of property ownership.