https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/lecture-7-solving-ax-0-pivot-variables-special-solutions/

 

Lecture 7: Solving Ax = 0: pivot variables, special solutions | Linear Algebra | Mathematics | MIT OpenCourseWare

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 nullspace. These video lect

ocw.mit.edu

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