Lecture 1: The Column Space of A Contains All Vectors Ax

Om kurset

Description In this first lecture, Professor Strang introduces the linear algebra principles critical for understanding the content of the course. In particular, matrix-vector multiplication \(Ax\) and the column space of a matrix and the rank. Summary Independent columns = basis for the column space Rank = number of independent columns \(A = CR\) leads to: Row rank equals column rank Related section in textbook: I.1 Instructor: Prof. Gilbert Strang