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

$(3,-1)$.
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 $(3,-1)$.