Linear Algebra: A Modern Introduction

Published by Cengage Learning

Chapter 2 - Systems of Linear Equations - 2.1 Introduction to Systems of Linear Equations - Exercises 2.1 - Page 63: 13

Answer

$\begin{bmatrix}x \\x \\ z\end{bmatrix}=\begin{bmatrix}4-2s-3t \\ s \\t\end{bmatrix}$; $t,s$ refer to real numbers.

Work Step by Step

Since we have $x+2y+3z=4$, this can be re-written as: $x=4-2y-3z$ Suppose $z =t, y= s$ Then: $x=4-2s-3t$ Our desired solution set is: $\begin{bmatrix}x \\x \\ z\end{bmatrix}=\begin{bmatrix}4-2s-3t \\ s \\t\end{bmatrix}$; $t,s$ refer to a real number.

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