Let u= (2,1,0,1,-1) and v=(-2, 3, 1, 0,2). Find scalars a and b so that au-bv=(-8,8,3,-1,7)

1 answer

au-bv = (2(a+b),a-3b,...) = (-8,8,...)
so,

2a+2b = -8
a-3b = 8

a=-1
b=-3

That fits the first two values. Does it also match the others?
yes. *whew*