Glossary math Term Page

Free Variable

A variable not fixed by pivots

free-variable #math#linear-algebra

Korean version

Aliases

free variable

Prerequisites

System of Equations

Related Concepts

Pivot Solution Set Null Space Rank Nullity

Core Idea

A free variable is a variable corresponding to a non-pivot column after elimination. Because it is not determined uniquely by the equations, it can vary and generate many solutions.

Role In This Blog

In Mathbong, free variables are used to explain infinite solution sets, null space structure, and nullity.

Posts Mentioning This Concept

[Linear Algebra Series Part 10] Gaussian Elimination: A Procedure for Solving and Reading Structure Learn Gaussian elimination as both a solving algorithm and a way to expose the structure of a linear system.[선형대수 시리즈 10편] 가우스 소거법: 해를 구하는 절차와 구조 읽기 가우스 소거법을 계산 알고리즘이자 해 구조를 드러내는 도구로 설명합니다.[Linear Algebra Series Part 11] When a System Has One Solution, No Solution, or Infinitely Many Classify the solution structure of a linear system using [[pivot|pivot]]s, [[free-variable|free variables]], and the shape of the reduced system.