An elementary proof using matrix theory is given for the following criterion: if "F"/"K" and "L"/"K" are field extensions, with "F" and "L" both contained in a common extension field, then "F" and "L" are linearly disjoint over "K" if (and only if) some…

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.

If f is a continuous positive-valued function defined on the closed interval from a to x and if k[subscript 0] is greater than 0, then lim[subscript k[right arrow]0[superscript +] [integral][superscript x] [subscript a] f (t)[superscript k-k[subscript 0]] dt= [integral][superscript x] [subscript a] f (t)[superscript -k[subscript 0] dt. This…