Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.1 Exercises - Page 11: 26

Answer

Example solution: \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 0&1\\ 0& 0 & 1&0\\ \end{bmatrix} \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 3&1\\ 0& 0 & 1&0\\ \end{bmatrix} \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 3&1\\ 4& 8 & 1&0\\ \end{bmatrix}

Work Step by Step

Construct an augmented matrix from the given solution set \begin{bmatrix} 1& 0 &0&-2\\ 0& 1 & 0&1\\ 0& 0 & 1&0\\ \end{bmatrix} To construct three different augmented matrices, perform different elementary row operations. Answers may differ. Example solution: R1=R1+2*R2 \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 0&1\\ 0& 0 & 1&0\\ \end{bmatrix} R2=R2+3*R3 \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 3&1\\ 0& 0 & 1&0\\ \end{bmatrix} R3=R3+4*R1 \begin{bmatrix} 1& 2 &0&0\\ 0& 1 & 3&1\\ 4& 8 & 1&0\\ \end{bmatrix}
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