V are vectors (one dimensional arrays).
C are coefficients (scalars).
These vectors are long, 40-50 entries per. So there are a large number of equations for 3 unknowns.
So I have four input vectors, and I want to solve for the three coefficients. Which ROOT function would be best to use for this?
You can use the functions of the matrix library to solve system of linear equations. Several type of matrix decompositions are available in ROOT, see the matrix package documentation, especially the paragraph on matrix decomposition