Explore the fundamental concepts of linear transformations in this comprehensive 7-hour course. Delve into topics such as graph representation, nullspace properties, and linear independence. Examine the Rank Nullity Theorem, Linear Extension Theorem, and coordinate systems. Investigate matrix operations, including multiplication and inverse matrices. Study isomorphisms, change of coordinates, and practical applications like reflections and projections. Learn how to integrate using coordinate transformations and discover the connections between linear algebra and calculus through derivative analysis.