Parametric Form

Introduction

Free Variables

Number of Solutions

A system in $x,y,z$ has reduced row echelon form

Which variable is free?

A system in $x_1,x_2,x_3$ has reduced row echelon form

How many solutions does the system have?

A system row reduces to

whose free variable is $z$. Enter $x$ as an expression in $z$ (for example: 2+3z).

A consistent system in $x_1,x_2,x_3,x_4$ has reduced row echelon form

How many free variables does it have? Enter a number.

Solve the system

and enter the parametric form of $x$ in terms of the free variable $y$ (for example: 1-2y).

In your own words, state the single most important definition or theorem of this section, and explain what it says.