Question

If 3(a,3,2)-2(3,b,b)=(-3,1,-2) determine a and b. Describe the set spanned by the vectors.

I don't know how to answer this

Answer 1

vectors are just a compact way of describing three independent sets of numbers. You just have

3a-6 = -3
9-2b = 1
6-2b = -2

clearly, a=1, and any value of b will work.

since (1,3,2) and (3,b,b) are not collinear, they span R2.