Finding 1-forms on Plane Vectors using dx1 and x2

[Thermodave]

Homework Statement

Given three vectors on a plane (x1,x2) with coefficients a and b:

v1 = a1*x1 + b1*x2
v2 = a2*x1 + b2*x2
v3 = a3*x1 + b2*x2 (presumably not used in this part)

Find the 1-forms (below) on the vectors.

Homework Equations

The given 1-forms are:
w1 = dx1
w2 = x2*dx1

The Attempt at a Solution

I can write w1=dx1 as,

dx1 = (dx1/dv1)*dv1 + (dx1/dv2)*dv2

This would seem to state dx1 in terms of a basis dv1, dv2. However, I still don't know x2. This is a problem from our last homework assignment that I didn't know how to do. I'm only posting it in this section because I'm sure we'll have more. Any help is appreciated.

 

[Thermodave]

Ok, so I'm pretty sure I'm not supposed to put dx in terms of dv1 since I have three vectors and it's only a 2D plane. So what does it mean to calculate the 1-form "on" a vector? Each vector obviously has a component in x1 and x2.