Column Space and Nullspace
In this linear algebra lesson, the instructor explains the concepts of vector spaces and subspaces, specifically focusing on the column space and null space of a matrix. He gives examples of vector spaces and subspaces and explains how to check for subspace properties. The instructor then moves on to the column space and demonstrates how it is a subspace of the vector space R4. He also shows how to determine which right-hand side vectors B allow for the solution of a linear equation system AX=B, revealing that solutions can only be found for B vectors that are in the column space.
Column Space and Nullspace -- Lecture 6. An explanation of vector spaces and subspaces. Especially the column space and nullspace of a matrix.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 16, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Column Space Java Applet - Java applet to play around with to investigate Column Spaces.
- What is a vector space?
- What is a vector subspace?
- What is a column space?
- What is a nullspace?
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Staff Review
The beginning of the meat of Linear Algebra, this video does a good job of explaining vector spaces, and subspaces (column spaces and nullspaces) and properties of them.
