Let u,v,w epsilon Rn be vectors. Then we have u - u u - w + w - v Let alpha i = (2, -1, 7, 3) . sigma 2 = (1, 4, 11, -2) and sigma 3 = (3, -6, 3, 8) be vectors in R4. Determine whether there exists a vector in S = { sigma 1 , sigma 2, sigma 3} which can be written as a linear combination of the other vectors in S. Hint: Solve for the scalars C1, C2, C3 for the vector equation of the vectors in S: c1 sigma1 + C2 sigma 2 + C3 sigma 3 = 0.
