Question

 Let W be the set of all vectors o the form

[ 5b + 2c

b

c ] where b and c are arbitrary. Find vectors u and v such that W = span{u, v}.

Answer 1

We have that

$$(5b+2c,b,c)=(5b,b,0)+(2c,0,c)=b(5,1,0)+c(2,0,1),$$

so then we have

$$W=\text{span}\{ (5,1,0),(2,0,1)\}$$

and the vectors that we find are:

$$u=(5,1,0),\quad v=(2,0,1).$$