STEM Lessons for College Students

Linear Algebra Example Problems – Matrix Column Space Basis and Dimension

Course website:

The column space of a matrix consists of all linear combinations of the matrices columns. In this video we show how to to find a basis to describe this subspace.

Simply perform row operations on A to obtain a reduced echelon form of the matrix. Identify the pivots in the reduced matrix. For each pivot location, grab the corresponding column in the original matrix. This collection of columns forms a basis for col(A) and the number of vectors/pivots is the dimension of the space.

If you enjoyed my videos please “Like”, “Subscribe”, and visit to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!

%d bloggers like this: