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 - 4.5 Basis and Dimension - 4.5 Exercises - Page 187: 31


$\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ does not form a basis for $R^2$.

Work Step by Step

From the figure, one can see that the set $\mathbf{v}_{1}=(1,1), \mathbf{v}_{2}=(2,2)$. It is easy to see that $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ are linearly dependent. Hence $\left\{\mathbf{v}_{1}, \mathbf{v}_{2}\right\}$ does not form a basis for $R^2$.
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