Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

Characteristic polynomials are used to determine when magic squares have magic inverses. A resulting method constructs arbitrary examples of such squares.

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)