## Differential Equations and Linear Algebra (4th Edition)

Published by Pearson

# Chapter 2 - Matrices and Systems of Linear Equations - 2.1 Matrices: Definitions and Notation - Problems - Page 121: 14

#### Answer

Column 3-vectors: $\begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}$ and $\begin{bmatrix} 3 \\ -2 \\ 6 \end{bmatrix}$ and $\begin{bmatrix} -4 \\ 5 \\ 7 \end{bmatrix}$ Row 3-vectors: $\begin{bmatrix} 1 & 3 & -4 \end{bmatrix}$ and $\begin{bmatrix} -1 & -2 & 5 \end{bmatrix}$ and $\begin{bmatrix} 2 & 6 & 7 \end{bmatrix}$

#### Work Step by Step

Column vectors With $j=1$ $\begin{bmatrix} a_{11} \\ a_{21} \\ a_{31}\end{bmatrix}=\begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}$ With $j=2$ $\begin{bmatrix} a_{12} \\ a_{22} \\ a_{32}\end{bmatrix}=\begin{bmatrix} 3 \\ -2 \\ 6 \end{bmatrix}$ With $j=3$ $\begin{bmatrix} a_{13} \\ a_{23} \\ a_{33}\end{bmatrix}=\begin{bmatrix} -4 \\ 5 \\ 7 \end{bmatrix}$ Row vectors With $i=1$ $\begin{bmatrix} a_{11} & a_{12} & a_{13}\end{bmatrix}=\begin{bmatrix} 1 & 3 & -4 \end{bmatrix}$ With $i=2$ $\begin{bmatrix} a_{21} & a_{22} & a_{23}\end{bmatrix}=\begin{bmatrix} -1 & -2 & 5 \end{bmatrix}$ With $i=3$ $\begin{bmatrix} a_{31} & a_{32} & a_{33}\end{bmatrix}=\begin{bmatrix} 2 & 6 & 7 \end{bmatrix}$

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