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Browse Classroom Capsules and Notes

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The author shows how to solve a class of analytic functions using an approach demonstrating a surprising connection between multivariable calculus and linear algebra.

The author describes a convenient method for calculating determinants where all entries on a given diagonal are equal and for some more general situations.

The author illustrates how certain determinants can be used to motivate students. The determinants in question have terms in artithmetic progressions.

The author provides a short proof of Cramer’s rule that avoids using the adjoint of a matrix.

Cramer's Rule gives an explicit formulation for the unique solution to a system of \(n\) equations in \(n\) unknowns when the coefficient matrix of the system is invertible.  The...

The author offers two examples that illustrate important central ideas in introductory linear algebra (independent or dependent vectors; invertible or singular matrices) which may aid students in...

A row (column) of a matrix is called “extraneous” if it is a linear combination of the other rows (columns).  The author shows that deleting an extraneous row or column of a...

In the game of tennis, if the probability that player \(A\) wins a point against player \(B\) is a constant value \(p\), then the probability that \(A\) will win a game from deuce is \(p^2/(1 - 2p...

The article answers negatively the question, “Is there a (non-trivial) linear transformation \(T\) from \(P_n\), the vector space of all polynomials of degree at most \(n\), to \(P_n\)...

The paper gives a short proof that for any \(n\) x \(n\) matrices \(A\) and \(C\) over a field of scalars, \(AC = I\) if and only if \(CA = I\). The proof relies on familiarity with...

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