# Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 85

In this capsule, proofs of the equivalence of the two definitions of the Fibonacci numbers are discussed. This helps the undergraduate view mathematics as a unified whole with a variety of...

The author shows that the system characterized by

$x(t) = a_1 t^2 + b_1 t + c_1$
$y(t) = a_2 t^2 + b_2 t + c_2$
$z(t) = a_3 t^2 + b_3 t + c_3$

must lie in a...

The Method of Undetermined Coefficients is approached by using linear operators and making use of patterns associated with matrix multiplication.  The authors discuss several pedagogical...

This article uses a generalization of a three-way gunfight to motivate the construction and solution to a first order linear system of difference equations.  The method of undetermined...

The authors show that a function between vector spaces that maps lines to lines is either a collineation or has one-dimensional range.

This article characterizes the points $(x, y)$ in the plane for which the determinant of a matrix of a particular form involving $(x, y)$ is $0$.  The matrices of interest have the...

Using L-U factorization, the author generates examples of matrices for which Gaussian elimination process can be done in integer arithmetic, including examples of matrices that are invertible...

The pseudo inverse of a matrix $A$ is used to obtain information about the rows of $A$.

The author characterizes and counts the number of the many row-reduced echelon forms associated with the set of all $m \times n$ matrices.

An interesting formula for the determinant of the sum of any two matrices of the same size is presented. The formula can be used to obtain important results about the characteristic polynomial...