Linear Algebra: A Modern Introduction

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

Chapter 1 - Vectors - 1.1 The Geometry and Algebra of Vectors - Exercises 1.1 - Page 17: 19

Answer

$\begin{bmatrix} 5\\1 \end{bmatrix}$

Work Step by Step

$u=\begin{bmatrix} 1\\ -1 \end{bmatrix}\;\;\;\;\;v=\begin{bmatrix} 1\\1 \end{bmatrix}\\\\ w=2u+3v\;\;\;{\color{Red}\Rightarrow } \;\;\;\;w= 2\begin{bmatrix} 1\\ -1 \end{bmatrix}\;\;+\;\;3\begin{bmatrix} 1\\1 \end{bmatrix}\\\\ w=\begin{bmatrix} 2\\-2 \end{bmatrix}\;\;+\;\;\begin{bmatrix} 3\\3 \end{bmatrix}\\\\ w\;\;=\;\;\begin{bmatrix} 2+3\\-2+3 \end{bmatrix}\;\;\;=\;\;\;\begin{bmatrix} 5\\1 \end{bmatrix}$
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