Answer
$(-2,2)$.
Work Step by Step
We know that $a(-1,3)+b(3,2)=(8,-2)$. Thus $-a+3b=8\\-3a+9b=24$ and $3a+2b=-2$.
Thus $-3a+9b+(3a+2b)=24+(-2)\\11b=22\\b=2$.
Thus $3a+2(2)=-2\\a=-2$
Thus the vector is $(-2,2)$.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 4 - Vector Spaces - 4.7 Change of Basis - Problems - Page 318: 3
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