Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 12


$S$ spans $R^2$.

Work Step by Step

Assume the combination $$a(2,0)+b(0,1)=(0,0).$$ We have the system \begin{align*} 2a&=0\\ b&=0. \end{align*} The above system has only the trivial solution, that is, $a=0, b=0$. Consequently, $S$ is linearly independent and since $R^2$ has the dimension $2$ then $S$ spans $R^2$.
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