The influential family that was a patron of the arts and played a significant role in the Renaissance in Florence was the Medici family.

The Medici family was a wealthy banking family that rose to power in Florence during the 15th century. They were not rulers in the traditional sense, but their wealth and influence allowed them to exert significant control over the city-state of Florence. The Medici family played a crucial role in the development of the Renaissance by providing patronage to artists, scholars, and architects.

Patronage of the Arts:
- The Medici family used their wealth to commission works of art and support artists. They believed that the arts were a reflection of their own prestige and power.
- They sponsored artists such as Michelangelo, Leonardo da Vinci, and Botticelli, who produced some of their most famous works under Medici patronage.
- The Medici family also established the Medici Bank, which became one of the most powerful financial institutions in Europe. This allowed them to fund their patronage of the arts and support the work of artists.

Support for Scholars and Learning:
- In addition to supporting artists, the Medici family also played a significant role in supporting scholars and promoting learning.
- They established the Medici Library, which became one of the largest and most important libraries in Europe at the time. The library housed a vast collection of manuscripts and books, making it a center of learning and scholarship.
- The Medici family also founded the Platonic Academy, a group of scholars and philosophers who met to discuss and study classical texts and ideas. This academy played a crucial role in the revival of interest in classical philosophy and literature during the Renaissance.

Political Influence:
- The Medici family's wealth and influence extended beyond the arts and scholarship. They held significant political power in Florence and used it to further their own interests.
- Several members of the Medici family served as rulers of Florence, including Lorenzo de' Medici, known as Lorenzo the Magnificent. During his rule, Florence experienced a period of great cultural and artistic flourishing.
- The Medici family also formed alliances and married into other powerful families, further expanding their influence in Italy and Europe.

In conclusion, the Medici family's patronage of the arts and support for scholars played a crucial role in the Renaissance in Florence. Their wealth and influence allowed them to support and promote the work of artists and scholars, contributing to a period of great cultural and intellectual growth in the city-state.