A First Course in Linear Algebra · Problem CRS.M20
Matrices — Robert Beezer
Mathematics — Linear Algebra · column-space-null-space-equal
Problem
Usually the column space and null space of a matrix contain vectors of different sizes. For a square matrix, though, the vectors in these two sets are the same size. Usually the two sets will be different. Construct an example of a square matrix where the column space and null space are equal.