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: 8


$$[x]_S=\left[ \begin {array}{ccc} -\frac{9}{2}\\ 29\\11\end {array} \right].$$

Work Step by Step

Since we have $$x= 2\left(\frac{3}{4},\frac{5}{2},\frac{3}{2}\right)+0\left(3,4,\frac{7}{2}\right)+4\left(-\frac{3}{2},6,2\right)=\left(-\frac{9}{2},29,11\right).$$ then we can write $x$ relative to the standard basis of $R^3$ as follows $$x= \left(-\frac{9}{2},29,11\right)=-\frac{9}{2}(1,0,0)+29(0,1,0)+11(0,0,1) .$$ Thus, he coordinates matrix of $x$ in $R^3$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} -\frac{9}{2}\\ 29\\11\end {array} \right].$$
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