# Browse Classroom Capsules and Notes

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Displaying 21 - 30 of 85

Given a square matrix $U$ and column vectors $\alpha$ and $\beta$, the author shows that $\det(U + \alpha \beta^T) = \det U + \beta^T$ Cof$(U) \alpha$.  This...

The author shows that every $2 \times 2$ real matrix with nonreal eigenvalues represents the composition of the following three operations: (1) a vertical “lift” to a plane...

Linear transformations satisfy properties of both additivity and homogeneity.  This capsule presents classes of functions that satisfy additivity but not homogeneity and vice versa....

This article provides a method for solving general linear systems via row reduction on special augmented matrices. This approach can avoid back substitution, but requires bigger matrices....

A technique is discussed for finding the eigenvalues of square matrices of small rank, which is useful for student discovery in a linear algebra class. The eigenvalues of a matrix of rank 1 or...

The author describes a method for constructing a smaller matrix with the same (or similar) eigenvalues that would be usable in the classroom. He illustrates this with matrices for Leslie...

The main object is to solve the inverse problem of recovering the original scene, represented by a vector or a matrix, from its photograph, represented by a product of a matrix and the...

Instead of using the image of a unit square in studying linear transformations in $R^2$, the authors show that looking at images of the unit circle yield an informative picture and...

Linear algebra is used to study financial trading strategies and expectations. Financial conditions are examined via matrix equations, using rank, column space, and null space arguments....

This article provides a proof of division algorithm in polynomial rings using linear algebra techniques. The proof uses the fact that polynomials of degree equal to and less than n form a...