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

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