# Linear Algebra Activities

free for use or modification in your classroom

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.pdf

# 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.pdf

# 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.pdf

# 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.pdf

# Analyzing traffic flow

Topics covered: Solving systems of linear equations

Outcomes: Students will learn how to solve a linear system and interpret its results. animations.pdf

# Computer animation

Topics covered: Linear transformations and matrix multiplication

Outcomes: Students will use linear transformations and matrix multiplication to move an object. LinearCodes.pdf

# 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. curvefitting.pdf

# 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.pdf

# 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. FibonacciBinet.pdf

# 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.pdf

# 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.pdf

# 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.pdf

# 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. AllPathsAlgorithm.pdf

# 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. GeneralizedAreas.pdf

# 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.