Answer
$(0,-3)$.
Work Step by Step
We know that $a(7,-1)+b(-9,-2)=(27,6)$. Thus $7a-9b=27$ and $-a-2b=6\\7a+14b=-42$.
Thus $7a+14b-(7a-9b)=-42-27\\23b=-69\\b=-3$.
Thus $7a-9(-3)=27\\7a=0\\a=0$
Thus the vector is $(0,-3)$.
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: 1
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