## Differential Equations and Linear Algebra (4th Edition)

Published by Pearson

# Chapter 4 - Vector Spaces - 4.4 Spanning Sets - Problems - Page 283: 37

#### Answer

$4$

#### Work Step by Step

We know that if $av_1+bv_2=v$, then $a+2b=3,-a+b=3,2a+3b=4$. Thus $(a+2b)+(-a+b)=3+3\\3b=6\\b=2$ $-a+b=-a+2=3\\a=-1$ And this satisfies the last equation because$2(-1)+3(2)=-2+6=4$

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