ou are asked to fit a circle with unknown radius but known center ( , ) to points (, ), [1, ]. Points on a circle satisfy: ( )2 ( )2 = . (a) Specify the over-constrained system of linear equations in matrix/vector form. If this is not possible, briefly explain why. (b) Complete the following if it is possible to solve the system: i. How many points are needed for the system to be over-constrained? Why? ii. Give the quadratic-error function for this least-squares estimator in matrix/vec- tor form. You need to specify the dimension of your matrices and vectors and their elements. iii. Differentiate this error function (in matrix/vector form) and set it equal to zero to obtain the normal equations. iv. Solve for . Show that the least-squares solution for the radius is simply the average distance of each point to the center