'1} Consider the following system of linear equations, with two parameters rub E R 2 l on: + 22 = I 23; + fig = 3 {a} Clamfy the above linear system of linear equations according to the values of the parameters a and b. \"1} Solve the above linear system of linear equations for the values of the parameters a and b for which there are innitely many solutions. [2} Consider the function {a} Prove that the limit mizmlrf} ay} exists. {b} Determine the points where the function f is continuous. It is necessary to justify the answer. [3} Consider the function a = cal3". {a} Study the subset of E2 where the function e is convex. {b} Compute Taylor's polynomial of order 2 of the function a at the point p = {ll1 ll}. [4} Consider the function Hz. 3;} = 1:3 + 2!}2 and the set A ={|[rr1 y} E R2 ::c2 + 3;: =1}. {a} 1|Write the Lagrange equations that determine the extreme points of f in the set A and find the solutions of the Lagrange equations. [11} Using the second order conditions1 classify the solutions obtained in part a} into local mandma and minima. Can you tell if one them is a global maximum or a minimum? Please. justify your answer. [5} Consider the function an y} = lll 53+ 2:2 + By they + 5:23}I + 2!}2 {a} Determine the critical points [if there are any} of the function f in the set R\". {b} Cla-Eify the critical points found in the previous part into {local or global} maxima, minima and saddle points