https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/resources/lecture-10-the-four-fundamental-subspaces/

 

Lecture 10: The four fundamental subspaces | Linear Algebra | Mathematics | MIT OpenCourseWare

For some vectors b the equation Ax = b has solutions and for others it does not. Some vectors x are solutions to the equation Ax = 0 and some are not. To understand these equations we study the column space, nullspace, row space and left nullspace of the m

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