Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.1 Matrices: Definitions and Notation - Problems - Page 121: 15

Answer

Column vectors: $\begin{bmatrix} 2 \\ 5 \end{bmatrix}$ and $\begin{bmatrix} 10 \\ -1 \end{bmatrix}$ and $\begin{bmatrix} 6 \\ 3 \end{bmatrix}$ Row vectors: $\begin{bmatrix} 2 & 10 & 6 \end{bmatrix}$ and $\begin{bmatrix} 5 & -1 & 3 \end{bmatrix}$

Work Step by Step

Column vectors With $j=1$ $\begin{bmatrix} a_{11} \\ a_{21} \end{bmatrix}=\begin{bmatrix} 2 \\ 5 \end{bmatrix}$ With $j=2$ $\begin{bmatrix} a_{12} \\ a_{22} \end{bmatrix}=\begin{bmatrix} 10 \\ -1 \end{bmatrix}$ With $j=3$ $\begin{bmatrix} a_{13} \\ a_{23} \end{bmatrix}=\begin{bmatrix} 6 \\ 3 \end{bmatrix}$ Row vectors With $i=1$ $\begin{bmatrix} a_{11} & a_{12} & a_{13}\end{bmatrix}=\begin{bmatrix} 2 & 10 & 6 \end{bmatrix}$ With $i=2$ $\begin{bmatrix} a_{21} & a_{22} & a_{23}\end{bmatrix}=\begin{bmatrix} 5 & -1 & 3 \end{bmatrix}$
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