Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - Review Exercises - Page 35: 35

Answer

Inconsistent.

Work Step by Step

Write the augmented matrix of the system of linear equations. $ \begin{bmatrix} 1 & 2 & 6 & 1\\ 2 & 5 & 15 & 4\\ 3 & 1 & 3 & -6 \end{bmatrix} $ Add -2 times the 1st row to the 2nd row to produce a new 2nd row. Add -3 times the 1st row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & 2 & 6 & 1\\ 0 & 1 & 3 & 2\\ 0& -5 & -15 & -9 \end{bmatrix} $ Add 5 times the 2nd row to the 3rd row to produce a new 3rd row. $ \begin{bmatrix} 1 & 2 & 6 & 1\\ 0 & 1 & 3 & 2\\ 0& 0 & 0 & 1 \end{bmatrix} $ Use back-substitution to find the solution. $0z=1 \rightarrow $ this equation is not possible $\rightarrow$ the system has no solution.
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