Problem N5 Let four vectors 1, 2, 3 and 4 be given by = (1,0,2), 2 = (0, 1, 1), 3 = (1,8,-6), 4 = (1,2,0); Let the vector space V be the linear span of 1, 2, 3 and 4. (a). Find all values of k such that the vector u = (2, 1, k) belongs to V. Explain. [Marks= 2] (b). Are the vectors {1, 2} linearly independent? Explain. [Marks=1] (c). Find the dimension and a basis of the space V. [Marks= 2] (d). Let A be the matrix whose columns are the vectors 1, 2, 3 and 4 (written as columns). Find a basis and the dimension of the solution set of the homogeneous linear system AX = 0. [Marks= 5]