Solving Linear Systems: Algebraic
https://maa.org/taxonomy/term/42315/all
enClassifying Row-Reduced Echelon Matrices
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/classifying-row-reduced-echelon-matrices
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author characterizes and counts the number of the many row-reduced echelon forms associated with the set of all \(m \times n\) matrices.</em></p>
</div></div></div>How to Determine Your Gas Mileage
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/how-to-determine-your-gas-mileage
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Two least-squares methods are used to estimate city and highway gas mileage from readily measured data. First, the author uses the standard least squares method which is suitable for a first linear algebra course. Second, the author discusses a more accurate weighted least squares method.</em></p>
</div></div></div>Starting with Two Matrices
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/starting-with-two-matrices
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>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 developing conceptual understanding before any general theory is attempted.</p>
</div></div></div>A Nonstandard Approach to Cramer's Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-nonstandard-approach-to-cramers-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>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 standard proof is developed using the adjoint matrix. In this capsule, the author uses properties of determinants and general matrix algebra to provide an alternative proof of Cramer's Rule.</em></p>
</div></div></div>An Alternate Proof of Cramer's Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-alternate-proof-of-cramers-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author provides a short proof of Cramer’s rule that avoids using the adjoint of a matrix.</em></p>
</div></div></div>Matrix Algebra Demos
https://maa.org/programs/faculty-and-departments/course-communities/matrix-algebra-demos
Linear Systems Applet
https://maa.org/programs/faculty-and-departments/course-communities/linear-systems-applet
Gaussian Elimination Applet
https://maa.org/programs/faculty-and-departments/course-communities/gaussian-elimination-applet
Matrix Online Calculator
https://maa.org/programs/faculty-and-departments/course-communities/matrix-online-calculator
Correcting Cramer's Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/correcting-cramers-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author clarifies the wording of Cramer's rule, sidestepping a common misconception. The Kronecker-Capelli theorem is introduced to help see Cramer's rule in a more complete context.</em></p>
</div></div></div>Classroom Capsules and Notes for Solving Linear Systems: Algebraic in Linear Algebra
https://maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-solving-linear-systems-algebraic-in-linear-algebra