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: 6


$$[x]_S=\left[ \begin {array}{ccc} 14\\ -11\end {array} \right].$$

Work Step by Step

Since we have $$x= -2( -1,4)+3(4,-1)=(14,-11).$$ then we can write $x$ relative to the standard basis of $R^2$ as follows $$x= (14,-11)=14(1,0)-11(0,1) .$$ Thus, he coordinates matrix of $x$ in $R^2$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 14\\ -11\end {array} \right].$$
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