Linear Algebra Activities
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The linear algebra activities below are designed for an introductory linear algebra class with a computation emphasis, whose only prerequisite is college algebra. These activities were developed through the support of NSF Award #1742304.
rowoperations.pdfThe Geometry of row operations
The Geometry of row operations
Topics covered: Elementary row operations
Outcomes: Students will investigate the geometry of linear systems and how row operations effect a linear system.
chemicalEquations.pdfBalancing chemical equations
Balancing chemical equations
Topics covered: Vector equations, solving systems using elementary row operations, and parameterized solution sets
Outcomes: Students will practice solving linear systems using elementary row operations, as well as converting between vector equations, matrix equations, and augmented matrices. Additionally, students will learn how to find particular solutions to a system from parameterized solution sets.
GPS.pdfHow does GPS work?
How does GPS work?
Topics covered: Solving systems of linear equations using a calculator
Outcomes: Students will learn how solving a system of linear equations can help identify their location. Students will practice how to use their calculators to solve more complicated systems of equations.
TrafficFlow.pdfAnalyzing traffic flow
Analyzing traffic flow
Topics covered: Solving systems of linear equations
Outcomes: Students will learn how to solve a linear system and interpret its results.
LinearCodes.pdfLinear block codes
Linear block codes
Topics covered: Matrix multiplication
Outcomes: Students will learn how to use matrix multiplication to encode data. They will also learn about error detection and the hamming distance.
AllPathsAlgorithm.pdfFinding all shortest paths in a network
Finding all shortest paths in a network
Topics covered: Matrix multiplication
Outcomes: Students will look at a modification of matrix multiplication to find all shortest paths in a graph.
animations.pdfComputer animation
Computer animation
Topics covered: Linear transformations and matrix multiplication
Outcomes: Students will use linear transformations and matrix multiplication to move an object.
curvefitting.pdfCurve fitting
Curve fitting
Topics covered: Matrix multiplication, transposition, and inverses
Outcomes: Students will learn how to use matrix operations to find a best fit curve.
LinesPlanes.pdfFinding equations of lines and planes with determinants
Finding equations of lines and planes with determinants
Topics covered: Determinants
Outcomes: Students will learn how to use determinants to find the equation of a line through two distinct points or the equation of a plan through three noncollinear points.
GeneralizedAreas.pdfGeneralizing areas of parallelograms
Generalizing areas of parallelograms
Topics covered: Determinants of 2x2 matrices
Outcomes: Students will think deeper about the applications of using determinants to calculate parallelograms by exploring how to calculate areas of more complicated shapes using determinants.
FibonacciBinet.pdfFibonacci numbers and Binet's formula
Fibonacci numbers and Binet's formula
Topics covered: Matrix multiplication and diagonalization
Outcomes: Students will develop Binet's formula by using matrix multiplication and diagonalization.
geneticInheritance.pdfGenetic inheritance with eigenvalues and eigenvectors
Genetic inheritance with eigenvalues and eigenvectors
Topics covered: Eigenvalues and eigenvectors
Outcomes: Students will use eigenvaluces and eigenvectors to predict long term characteristic development in a species.
PredatorPreyModel.pdfModeling predator-prey dynamics
Modeling predator-prey dynamics
Topics covered: Eigenvalues and eigenvectors
Outcomes: Students will use eigenvaluces and eigenvectors to predict the effects of predator-prey dynamics on two species.
RankingSportsTeams.pdfRanking sports teams
Ranking sports teams
Topics covered: Eigenvalues and eigenvectors
Outcomes: Students will use eigenvaluces and eigenvectors to rank sports teams in a league based on their regular season win-loss data.
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