Linear Equations

Matrix form, vector form and solution structure

This chapter presents linear equation systems in matrix form and vector form, then solves them using reduced row echelon form, highlighting the three cases: unique solution, no solution and infinitely many solutions.

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Chapter contents

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Topic	Pages
Matrix representation of equation system	1
Vector representation of equation system	2
Solving [A \| b] using RREF	3
Case 1: unique solution	4
Geometric example of unique solution in 2D	5–7
Case 2: no solution	8–9
Case 3: infinitely many solutions	10–12
Geometric example of infinitely many solutions in 2D	13–14
Summary for case 3 with infinite solutions	15
From infinite solutions case to domain of n×n square matrix A	16–17

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