Answer
$(3,-1)$.
Work Step by Step
We know that $a(2,-2)+b(1,4)=(5,-10)$. Thus $2a+b=5$ and $-2a+4b=-10$.
Thus $2a+4b+(-2a+b)=5+(-10)\\5b=-5\\b=-1$.
Thus $2a+(-1)=5\\a=3$
Thus the vector is $(3,-1)$.
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: 2
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