A First Course in Linear Algebra · Problem CRS.C52
Matrices — Robert Beezer
Mathematics — Linear Algebra · column-space-consistency
Problem
The following archetypes are systems of equations. For each different coefficient matrix build two new vectors of constants. The first should lead to a consistent system and the second should lead to an inconsistent system. Descriptions of the column space as spans of linearly independent sets of vectors with ``nice patterns'' of zeros and ones might be most useful and instructive in connection with this exercise. (See the end of Example CSROI.)
Archetype A, Archetype B, Archetype C, Archetype D/Archetype E, Archetype F, Archetype G/Archetype H, Archetype I, Archetype J