Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4-5 - Cumulative Test - Page 289: 3

Answer

No possible linear combination.

Work Step by Step

Let $v_1$ be the first column vector and $v_2$ be the second one, $v_3$ be the third one. Let $av_1+bv_2=v_3$. Then $a+2b=3$, $7a+8b=9$, $4a+5b=7$ are the equations we have to satisfy. Thus $a=3-2b$, thus $7(3-2b)+8b=9\\21-14b+8b=9\\12=6b\\b=2$ Thus $a=3-2(2)=-1$ We have to check if this solution satisfies the third equation. $4a+5b=4(-1)+5(2)-4+10=6\ne7$. Thus, there is no possible linear combination.
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