Abstract
Most introductory linear algebra books contain examples and exercises in which they ask for conditions on the right-hand side of a linear system to ensure consistency. The usual recommendation is to reduce the system Ail = b by elemen? tary row operations to a form f/x = c, where U is an echelon matrix, and set the components of c that correspond to the zero rows of U equal to zero. Since c is obtained from b by elementary row operations, we thus obtain a set of homoge? neous linear equations for the components of b. It is then natural to ask questions about this system such as: Are its equations independent and what characterizes its coefficient matrix?
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