Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - Problems - Page 32: 4

Answer

$$u=\begin{bmatrix} 3 \\ 2\\ \end{bmatrix} , v=\begin{bmatrix} 2 \\ -1\\ \end{bmatrix} , -v=\begin{bmatrix} -2 \\ 1\\ \end{bmatrix}, -2v=\begin{bmatrix} -4\\ 2\\ \end{bmatrix}, $$$$ u+v=\begin{bmatrix} 5 \\ 1\\ \end{bmatrix}, u-v=\begin{bmatrix} 1 \\ 3\\ \end{bmatrix}, u-2v=\begin{bmatrix} -1 \\ 4\\ \end{bmatrix} $$

Work Step by Step

Addition and subtraction operations are carried out by adding or subtracting corresponding entries in the matrix, while scalar multiplication distributes the scalar to each entry in the matrix: $$u=\begin{bmatrix} 3 \\ 2\\ \end{bmatrix} , v=\begin{bmatrix} 2 \\ -1\\ \end{bmatrix} , -v=\begin{bmatrix} -2 \\ 1\\ \end{bmatrix}, -2v=\begin{bmatrix} -4\\ 2\\ \end{bmatrix}, $$$$ u+v=\begin{bmatrix} 5 \\ 1\\ \end{bmatrix}, u-v=\begin{bmatrix} 1 \\ 3\\ \end{bmatrix}, u-2v=\begin{bmatrix} -1 \\ 4\\ \end{bmatrix} $$ Graphing the vectors requires the first entry of the matrix to be taken as an x-coordinate and the second entry of the matrix to be taken as the y-coordinate, then graphing as an ordered pair (with an arrow).
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