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: 18

Answer

No. The planes do not have a point of intersection; i.e., the system of equations is not consistent.

Work Step by Step

Simplifying the augmented matrix to triangular form provides the relations: $x_1=\frac{-14}{6}$, $x_2=\frac{-5}{6}$, and $0=\frac{-5}{6}$. This final condition is not true, so there is no $(x_1, x_2)$ such that the equations for the three specified planes are satisfied.
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