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 - 4.7 Coordinates and Change of Basis - 4.7 Exercises - Page 210: 7


$$[x]_S=\left[ \begin {array}{ccc} 5\\ 4\\3\end {array} \right].$$

Work Step by Step

Since we have $$x= 2(1,0,1)+3(1,1,0)+(0,1,1)=(5,4,3).$$ then we can write $x$ relative to the standard basis of $R^3$ as follows $$x= (5,4,3)=5(1,0,0)+4(0,1,0)+3(0,0,1) .$$ Thus, he coordinates matrix of $x$ in $R^3$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 5\\ 4\\3\end {array} \right].$$
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