Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 2 - Systems of Linear Equations - 2.1 Introduction to Systems of Linear Equations - Exercises 2.1 - Page 63: 12

Answer

$\begin{bmatrix}x_1 \\x_2\end{bmatrix}=\begin{bmatrix}\dfrac{-3}{2}t+\dfrac{5}{2} \\ t\end{bmatrix}$; $t$ refers to a real number.

Work Step by Step

Since we have $2x_1+3x_2=5$, this can be re-written as: $x_1=\dfrac{-3}{2}x_2+\dfrac{5}{2}$ Suppose $x_2=t$ Then: Our desired solution set is: $\begin{bmatrix}x_1 \\x_2\end{bmatrix}=\begin{bmatrix}\dfrac{-3}{2}t+\dfrac{5}{2} \\ t\end{bmatrix}$; $t$ refers to a real number.
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