Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.3 Exercises - Page 33: 20

Answer

The Span$\{V_{1}, V_{2}\}$ is the $xz$ plane.

Work Step by Step

Since the $y$-coordinate in both vectors is zero, it follows that the $y$-coordinate in any linear combination of $V_{1}$ and $V_{2}$ would have zero value. In other words, Span$\{V_{1}, V_{2}\}$ is made up of all the vectors in the space $\mathbb{R}^{3}$ that have zero $y$-coordinates. This is precisely the $xz$ plane.
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