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MATH-504In Development

Calculus & University Mathematics

Linear Algebra

Use vectors, matrices, transformations, and eigen ideas to solve systems and describe higher-dimensional structure.

Level
Level 5 — Higher Mathematics
Learning time
20 hours
Format
Extended Course
Modules
10

Course structure

A clear outline before lessons begin.

This course is published as a development map. Full lessons, practice, and assessments will be added after content review.

Prerequisites

Complete these courses before beginning when they are available.

Recommended preparation

These courses strengthen preparation but are not strict prerequisites.

Learning outcomes

By the end, learners will be able to…

  • Solve systems of linear equations using row reduction and matrix methods.
  • Work with vectors, spans, independence, bases, and dimension.
  • Represent linear transformations with matrices and determinants.
  • Compute and interpret eigenvalues and eigenvectors in basic settings.
  • Use orthogonality and least-squares ideas in approximation problems.
  • Model a practical relationship with a linear algebra framework.

Module outline preview

10 planned modules

Estimated times add up to the course’s planned learning time. Every module is in development.

  1. 01

    Vectors, Matrices, and Linear Structure

    Introduce vector notation, matrices, and linear combinations.

    2 hours · In Development
  2. 02

    Systems and Row Reduction

    Solve systems systematically with elimination and row-echelon form.

    2 hours · In Development
  3. 03

    Matrix Operations and Inverses

    Use matrix arithmetic and inverse methods where appropriate.

    2 hours · In Development
  4. 04

    Determinants and Geometric Meaning

    Calculate determinants and interpret their structural significance.

    2 hours · In Development
  5. 05

    Vector Spaces and Independence

    Determine span, linear independence, and subspace structure.

    2 hours · In Development
  6. 06

    Bases and Dimension

    Choose useful coordinates and describe the size of a vector space.

    2 hours · In Development
  7. 07

    Linear Transformations

    Represent, compose, and interpret transformations with matrices.

    2 hours · In Development
  8. 08

    Eigenvalues and Eigenvectors

    Analyze directions and scale factors preserved by transformations.

    2 hours · In Development
  9. 09

    Orthogonality and Least Squares

    Approximate data or systems using projections and orthogonal structure.

    2 hours · In Development
  10. 10

    Linear Algebra Applications Synthesis

    Apply matrices and vectors to a cumulative model or decision problem.

    2 hours · In Development

Course status

Course coming soon

This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.

Back to Mathematics

Recommended learning paths

A clear sequence, not a random list.

These paths show a recommended order. Branches identify connected study that can follow once prerequisites are complete.