We apply the method of elimination to all matrices, invertible or not. Counting the pivots gives us the rank of the matrix. Further simplifying the matrix puts it in reduced row echelon form R and improves our description of the null space.
Lecture Video and Summary
- Watch the video lecture Solving Ax = 0: Pivot Variables, Special Solutions (00:43:20)
Solving Ax = 0: Pivot Variables, Special Solutions
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
- Read Section 3.2 in the 4th or 5th edition.
Problem Solving Video
Problems and Solutions
Work the problems on your own and check your answers when you're done.