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: 19

Answer

A line through $\begin{bmatrix}8\\2\\-6\end{bmatrix}$

Work Step by Step

Since $v_2=1.5v_1$, the span of $\{v_1, v_2\}$ is merely the set of vectors that are scalar multiples of $v_1$. This can be clearly shown, for any vector $v_3$ in the span of $\{v_1, v_2\}$, where $a$, $b$, and $c$ are real numbers: $$v_3 = av_1 + bv_2 = av_1 + 1.5bv_1 = (a+1.5b)v_1 = cv_1$$
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