The document considers whether there are always two different combinations of vectors u, v, and w in a plane that produce a given vector b. It sets up a system of equations using the vectors (1,3), (2,7), (1,5) and the target vector b=(0,1). There are three unknowns but only two equations, meaning there are infinite solutions. By setting one variable to 0 and solving, one combination is found to be -2, 1, 0. Setting a different variable to 1 yields another combination of 1, -1, 1.