Determine whether the vector w 3 5 1 is in the span of the

Determine whether the vector w = (3, 5, 1) is in the span of the following vectors: v_1 = (1, 1, 1), v_2 = (2, 3, 1), v_3 = (0, -1, 1)

2v_1-v_2=(0,-1,1)=v_3

So the vectors are linearly dependent

So if w is to be in the span of the given three vectors then it must also be in the span of v1 and v2

Let, w=av1+bv2

(3,5,1)=a(1,1,1)+b(2,3,1)

3=a+2b

5=a+3b

1=a+b

Solving gives:a=-1,b=2

So,

w=-v1+2v2