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: 46

Answer

the set of vectors is linearly independent set of vectors.

Work Step by Step

Consider the combination $$a \left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]+b\left[\begin{array}{cc}{0} & {1} \\ {0} & {0}\end{array}\right]+c\left[\begin{array}{ll}{0} & {0} \\ {0} & {0}\end{array}\right]=0, \quad a,b,c\in R.$$ Which yields the following system of equations \begin{align*} a&=0\\ b&=0. \end{align*} Then the set of vectors is linearly independent set of vectors.
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