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 - Review Exercises - Page 222: 53


$$[x]_S=\left[ \begin {array}{ccc} 8\\ -2\end {array} \right].$$

Work Step by Step

Since we have $$x= 3(1,1)+5(1,-1)=(8,-2).$$ then we can write $x$ relative to the standard basis of $R^2$ as follows $$x= (8,-2)=8(1,0)-2(0,1) .$$ Thus, he coordinates matrix of $x$ in $R^2$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 8\\ -2\end {array} \right].$$
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