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 10: 7


Row three has no solution therefore the matrix is inconsistent.

Work Step by Step

The long form of row three in the given matrix is expressed by the following: $0x_{1} + 0x_{2} + 0x_{3} = 1 $ For any values of $x_{1},x_{2},x_{3}$, the following result occurs: $0\times x_{1} + 0\times x_{2} + 0\times x_{3} = 1 $ $0+0+0=1$ $0=1$, which is false As it is not possible to find any values to make the previous statement true, there is no solution thus making the system inconsistent.
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