Final answer:
The lack of patronage, cultural dependence on Europe, and absence of first-rate art schools and museums were the greatest inhibiting factors for American artists in the first half of the nineteenth century.
Step-by-step explanation:
The greatest inhibiting factor for American artists in the first half of the nineteenth century was the lack of adequate patronage from the wealthy or the government, which limited their opportunities for financial support and recognition. American artists faced difficulty in finding wealthy patrons who could commission their work or provide financial backing. Additionally, the government did not provide sufficient support for the arts during this time period.
Furthermore, the cultural dependence on Europe also posed a challenge for American artists. Many artists felt the need to go to Europe to receive proper art education and exposure to great art, as there were no first-rate art schools or museums in America until later in the century. American artists' reliance on European models and styles hindered their ability to develop their own distinct artistic identity.
In conclusion, the lack of adequate patronage, cultural dependence on Europe, and absence of first-rate art schools and museums were the main inhibiting factors for American artists in the first half of the nineteenth century.