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: 9


the vectors of $S$ are not linearly independent.

Work Step by Step

The set $S=\{(-4,5),(0,0)\}$ is not a basis for $R^2$ because the vectors in $S$ are not linearly independent. Indeed, considering the linear combination $$c_1 (-4,5)+c_2(0,0)=(0,0),$$ then the choice $c_1=0$ and any non-zero value for $c_2$ satisfies the above combination. Hence, the vectors of $S$ are not linearly independent.
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