HOTS-LA-001

Matrix Systems Explorer

An interactive exploration of how matrices can represent, analyse, classify and solve systems of linear equations.

Equations → AX = B → Determinant → Rank → Classification → Solution

The Investigation

A system of linear equations can be represented compactly using the matrix equation:

A X = B

This explorer investigates the mathematical structure of the system using determinants, inverses and matrix rank.

INTERACTIVE TOOL

Explore a Linear System

Enter the coefficients of a system of linear equations and analyse its mathematical structure.

System Size

Enter the System

Define the coefficients and constants.

System Analysis

Mathematical properties and results.

∑

Enter a system and click Analyse System.

Matrix Representation

Matrix Properties

det(A) —

rank(A) —

rank([A|B]) —

Unknowns —

Inverse of A

System Classification

Solution

Mathematical Interpretation

THE PROCESS

How the Explorer Thinks

Represent

Convert equations into the matrix equation AX = B.

→

Analyse

Calculate determinant, inverse and matrix rank.

→

Compare

Compare rank(A) with rank([A|B]).

→

Conclude

Determine whether the system has one, infinitely many or no solutions.

CONCEPTS CONSOLIDATED

What This Study Connects

Matrix Algebra Determinants Matrix Inverse Rank Augmented Matrix Linear Systems

A system of equations is not merely a collection of equations. It can be represented as a matrix structure whose determinant, inverse and rank reveal fundamental properties of its solution.

HOTS REFLECTION

From Study to Deliverable

This explorer was developed as a technical deliverable following an intensive study of Linear Algebra. The objective was to transform mathematical concepts into an interactive, explainable system.

Learn → Understand → Build → Explain → Document