Linear Algebra I

Created by: University of Waterloo, powered by Möbius

Description

The Linear Algebra I Content Pack is a Möbius course developed by the University of Waterloo that you can use as a customizable starting point to a complete linear algebra course in Möbius. This Content Pack explores: systems of linear equations, matrix algebra, determinants, and introduces vector spaces and their applications. This customizable resource contains 9 units of sectioned lessons and assignments enhanced with Möbius capabilities including algorithmic questions, in-lesson questions with unlimited practice, adaptive questions, interactive narratives, Geogebra resources, hints and immediate feedback, and end-of-section assignments.

How does Möbius take the University of Waterloo’s content to the next level?

  • Lessons contain interactive elements like Interactive Narratives, HTML objects, Math Apps, or Geogebra applications to help solidify difficult STEM concepts.

  • Learn how Möbius’ unique STEM question types throughout this content provide the best STEM learning experience.

  • Work with over 50 configurable assessment properties when modifying existing or building your own assessments.

Course Structure

  • All content is organized into 9 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 43 lessons that promote Active Learning by including illustrative visualizations, interactive elements, and example problems with immediate feedback
  • Different forms of assessment materials are distributed across 8 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 670 questions that you can use to create your own lessons and assignments or supplement existing ones
9 units
43 lessons
8 assignments
670+ questions

Unit 1: Vectors in Rn

  • 1a Geometry, Lines, and Planes in Rn

  • 1b Norm, Dot Product, and Cross Product

  • 1c Vector Projections

  • 1d Putting It All Together

Unit 2: Systems of linear equations

  • 2a Systems of Linear Equations

  • 2b Augmented and Coefficient Matrices, Reduced Row Echelon Form, and Gaussian Elimination

  • 2c Homogeneous and non-homogeneous systems

  • 2d Putting It All Together

Unit 3: Matrix Algebra

  • 3a Matrix Algebra

  • 3b Special Matrices

  • 3c Matrix-Vector Multiplication

  • 3d Matrix Multiplication

  • 3e Matrix Inverse

  • 3f Putting It All Together

Unit 4: Independence and Basis

  • 4a Linear Combinations and Span

  • 4b Linear Dependence and Linear Independence

  • 4c Basis

  • 4d Coordinates

  • 4e Change of Basis Matrix

  • 4f Putting It All Together

Unit 5: Subspaces of Rn

  • 5a Subspaces of Rn

  • 5b Basis and Dimension

  • 5c Fundamental Subspaces of a Matrix

  • 5d Putting It All Together

Unit 6: Linear Transformations on Rn

  • 6a Linear Mapping

  • 6b Matrix of a Linear Mapping

  • 6c Composition of Transformations and Matrix Products

  • 6d Function Basics

  • 6e Special Spaces (Kernel, Range)

  • 6f Special Transformations (Rotations, Projections, Reflections)

  • 6g Putting It All Together

Unit 7: Determinants

  • 7a Finding Determinants via Cofactor Expansion

  • 7b Finding Determinants via Row Reduction

  • 7c Properties of Determinants

  • 7d Area and Volume

  • 7e Cramer’s Rule

  • 7f Putting It All Together

Unit 8: Diagonalization

  • 8a Eigenvalues and Eigenvectors

  • 8b Finding Eigenvalues and Eigenvectors

  • 8c Diagonalization

  • 8d Applications

  • 8e Putting It All Together

Quizzes

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