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 221: 9


$$v=2 u_1-u_2+3u_3.$$

Work Step by Step

Suppose the following linear combination $$(3,0,-6)=a(1,-1,2)+b(2,4,-2)+c(1,2,-4), \quad a,b,c\in R.$$ Which yields the following system of equations \begin{align*} a+2b+c&=3\\ -a+4b+2c&=0\\ 2a-2b-4c&=-6. \end{align*} Solving the above system, we get the solution $a=2$, $b=-1$, $c=3$. Hence, $$v=2 u_1-u_2+3u_3.$$
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