Suppose we are asked to fit a straight line to the following data m 2 1 3 -2 1 2 -1 1 so that mx + c = y Write the system of linear equations mx + c = y. Determine the matrix A. and vector b to write this problem as a matrix equation A x b Describe the relationship between the vector b and the column space of (a) (b) A. Given that the matrix equation in part (a) has no solution, a least squares solution is sought by looking for a vector x that minimises the error e = Ax - b. This means that e is perpendicular to the columns of A. Show that this fact leads to the normal equations: (c) ATA X = ATb Use the matrix equation in part (c) to determine the associated normal equations and the least squares solution, x, for the matrix equation in part (a). (d)