Let W be the set of all vectors of the form [-2a-4b, -a, b].Find vectors u and v in R³ such that W = span {u, v}.

Answer 1

Express vectors in W as a linear combination of two vectors.

A vector in W has the form:

[-2a - 4b] [-2a] [-4b] [-2] [-4]

[ -a ] = [-a ] + [ 0 ] = [ -1]a + [ 0]b

[ b ] [ 0 ] [ b ] [ 0 ] [ 1]

Therefore:

u = [-2, -1, 0] and v = [-4, 0, 1]

So W = span{u, v}.