Dive into the fundamentals of linear algebra in this comprehensive 90-minute tutorial. Begin with an introduction to vectors, exploring their length in 2D space through practical examples. Progress to vector operations including addition, scalar multiplication, and subtraction. Expand your understanding to 3D vectors and the concept of R^n. Learn to calculate vector lengths and delve into proofs of vector properties such as commutativity and associativity. Explore the dot product, its definition, and its application in finding angles between vectors. Discover orthogonal vectors and conclude with a proof about parallelogram diagonals, building a solid foundation in essential linear algebra concepts.