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参数形式

1. Introduction

Introduction

Free Variables

Number of Solutions

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

\left(\begin{array}{ccc|c} 1 & 0 & 5 & 1 \\ 0 & 1 & 2 & -1 \end{array}\right).

Which variable is free?

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

\left(\begin{array}{ccc|c} 1 & 2 & 0 & 4 \\ 0 & 0 & 1 & 5 \end{array}\right).

How many solutions does the system have?

A system row reduces to

\left(\begin{array}{ccc|c} 1 & 0 & -3 & 2 \\ 0 & 1 & 4 & 5 \end{array}\right),

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

\left(\begin{array}{cccc|c} 1 & -2 & 0 & 3 & 1 \\ 0 & 0 & 1 & 4 & -1 \end{array}\right).

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

Solve the system

\left\{\begin{aligned} x + 2y + z &= 4 \\ 3x + 6y + 2z &= 9 \end{aligned}\right.

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

The reduced row echelon form of a consistent system has one free variable. What is the shape of the solution set?

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

\left(\begin{array}{ccc|c} 1 & 0 & 2 & -1 \\ 0 & 1 & 1 & 3 \end{array}\right).

Solving with $z$ as the free variable, enter the expression for $x$ .

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