Vectors are easier to understand when they’re described in terms of orthogonal bases. In addition, the Four Fundamental Subspaces are orthogonal to each other in pairs. If A is a rectangular matrix, Ax = b is often unsolvable.

These video lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook. However, this book is still the best reference for more information on the topics covered in each lecture.

Strang, Gilbert. Introduction to Linear Algebra. 5th ed. Wellesley-Cambridge Press, 2016. ISBN: 9780980232776.

Instructor/speaker: Prof. Gilbert Strang