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: 27



Work Step by Step

The system is consistent for all values of $f$ and $g$, so it cannot be inconsistent for any values of $f$ and $g$. For the system to be inconsistent, it would require the left hand side of the second equation to be a scalar multiple of the left hand side of the first, with different right hand values. The condition $\frac{c}{d}\neq\frac{1}{3}$ ensures that the above cannot occur, ensuring consistency.
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