Vector Approximation and Distance Calculation

This lecture covers the concept of finding the best approximation of a vector by a linear combination of other vectors, as well as calculating the distance between a vector and a subspace spanned by given vectors. The instructor presents step-by-step solutions to exercises involving vector approximations and distance calculations, emphasizing the importance of orthogonal projections and vector spaces. Various methods and formulas are demonstrated to determine the closest vector approximation and distance, providing a comprehensive understanding of vector operations and geometric interpretations.