M lab - a.( X Edufide X G G gmail - X C image X Design X G curvatu X curvatu X M Math - X G math fc x e OA12 ( X Course X C Let L:R X V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=8 *IA : (a) A square matrix A has the characteristic polynomial PA ( 1) = (1 - 3)2(1 - 5) 10 ( 1 + 4) 3 Then A is a matrix. on The eigenvalues of A and their algebraic multiplicities are (list eigenvalues in the order least to greatest): 1. Al = with algebraic multiplicity 2. 12 = with algebraic multiplicity 3. 13 = with algebraic multiplicity (b) Suppose that B is a 6 x 6 matrix with rank(B) = 2. Find the geometric multiplicity of the eigenvalue > = 0 of B. Geometric multiplicity Check Mostly clear Q Search W ENG 11:19 PM US 2023-04-05 53M lab - a.( X Edufide X G G gmail - X C image X Design X G curvatu x curvatu X M Math - X G math fc x e OA12 ( X Dashbc X C Let L:R X V X eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852&page=9 *IA : -7 0 18 Let A = -6 2 12 -3 8 The eigenvalues of A are 1 = -1 and 1 = 2. (a) Find a basis for the eigenspace E-1 of A associated to the eigenvalue 1 = -1 BE-1 (b) Find a basis of the eigenspace E2 of A associated to the eigenvalue 1 = 2. BE = -30 C Mostly clear Q Search ENG 11:20 PM US 2023-04-05 3M lab - a.( X Edufide x G G gmail - X C image X Design X G curvatu x curvatu X M Math - X G math fc x e OA12 ( X * Dashbc X C Let L:R X + V X F -> C eclass.srv.ualberta.ca/mod/quiz/attempt.php?attempt=12777327&cmid=6755852 * IA : Qu In R', let R be the rotation about the origin through the angle 27 /3. Then the standard matrix [ R] representing R is cos(2*pi/3) -sin(2*pi/3) [R] = sin(2*pi/3) cos(2*pi/3) on Fini Your last answer was interpreted as follows: cos ( 2;7 ) - sin (257 ) sin ( 2;" ) cos (27 ) (Leave your answer in terms of sin and cos. You can enter 7 as pi.) Consequently R transforms the vector (5, 5) into O 0 Your last answer was interpreted as follows: [o o] Your answer is partially correct. Something isn't right here. Please try again. Try again -30 C Mostly clear Q Search ENG 11:20 PM US 2023-04-05 3