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: 16

Answer

\begin{array}{l}{\qquad A=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4} \\ {5} & {1}\end{array}\right]} \end{array} The column vectors \begin{array}{l} {\qquad \mathbf{b}_{1}=\left[\begin{array}{l}{1} \\ {3} \\ {5}\\ \end{array}\right]}\\ {\qquad \mathbf{b}_{2}=\left[\begin{array}{l}{2} \\ {4} \\ {1}\\ \end{array}\right]}\end{array}

Work Step by Step

Given \begin{array}{l}{a_{1}=[1.2]} \\{a_{2}=[3.4]} \\ {a_{3}=[5.1]}\end{array} So, The appropriate matrix for the given row vectors is: \begin{array}{l}{\qquad A=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4} \\ {5} & {1}\end{array}\right]} \end{array} The column vectors for this matrix are: \begin{array}{l} {\qquad \mathbf{b}_{1}=\left[\begin{array}{l}{1} \\ {3} \\ {5}\\ \end{array}\right]}\\ {\qquad \mathbf{b}_{2}=\left[\begin{array}{l}{2} \\ {4} \\ {1}\\ \end{array}\right]}\end{array}
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