question 8 For a non-homogeneous linear system with 25 equations and 15 answer the following questions. 1-Can the system be incompatible? 2-Can the system have an infinite number of solutions? 3- Can the system have a unique solution?

question 9

(a) [2 points] Give the characteristic polynomial of A and deduce that the eigenvalues of A are eigenvalues of A are 8 and 11. (b) [3 points] For each of the eigenvalues found in part (a), give a basis of the associated eigen space. (c) [2 points] Determine if the matrix A is diagonalizable. If you say that it is, find an invertible matrix P and a diagonal matrix D such that A = P DP 1

Question 9. [7 points] Considerer la matrice 9 1 1 A = 1 9 1 1 9 (a) [2 points] Donner le polynome caracteristique de A et en deduire que les valeurs propres de A sont 8 et 11. (b) [3 points] Pour chacune des valeurs propres trouvees a la partie (a), donner une base de l'espace propre associe. (c) [2 points] Determiner si la matrice A est diagonalisable. Si vous dites qu'elle l'est, trouver une matrice inversible P et une matrice diagonale D telle que A = PDP-1