Browse Classroom Capsules and Notes

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Displaying 71 - 80 of 85

The article illustrates the notion of eigenvalue and its corresponding eigenvector using hands of an analog clock. This capsule deals with $2 \times 2$ real matrices, single eigenvalues, and...

This capsule points out several potential confusions in commonly used linear algebra notation.

Given a unit vector $p$ in $\mathbf{R}^3$ and an angle $\theta$, what is the matrix of the rotation of $\mathbf{R}^3$ about $p$ through an angle of $\theta$ in terms of 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 $A$.

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...

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...

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...