# Browse Classroom Capsules and Notes

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Displaying 51 - 60 of 85

An elementary argument, different from the usual one, is given for the familiar equality of row and column rank. The author takes “full advantage of the following two elementary...

A Markov chain with 9 states is used to illustrate a technique for finding the fundamental matrix.

The author presents a visual proof that the determinant of a 2 by 2 matrix equals the area of the corresponding parallelogram.

The author gives an alternative to the usual Gram-Schmidt process and shows how to obtain the “QR Factorization” by using pairs of row column operations.

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...

Motivated by the interpretation of a determinant of a $2 \times 2$ matrix as the area of a parallelogram, the author derives Cramer's rule geometrically.

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....

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

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...