T-1 2 5 ſi 0 0] Q2. (19 pts) Let B 0 1 8 and C = 6 3 0 0 0 1 5 4 1] determinants using the properties of determinants: Compute the following a) det($_35") b) det(3C) c) det(B25) d) det (((3C)B)')
linear algebra 3. Let A be the following matrix: A= 0 -2 6 0 0 C 6 C 02 0 0 8 0 0 5 T 3 -1 7 6 2 - 4 04 (a) Find det(A). Show your work Express your answer in terms of x. (b) Identify the value(s) of x for Nul (A) = {0}.
2 1 -2 3 0 1 4 2 1. Let B -3 0 3 ( 1) 2 2 -1 0 (a) Find det(B).(Show all work.) -3 -R2- .A 4 O0-2/2 1-3 0 3 入ス-1 0 I-2 3 det ao -1 O 3 1-3 RyR-( 2 2-10 420 4 (b) Find det(BT). (c) Find det(B-1). (d) Find det(-B) . (e) Is 0 an eigenvalue of B? (f) Are thè columns of B linearly independent?
0 -1 5 6 -3 6 Let C = and D = 7 4 0 1 4 0 Find -6C+ 3D □□□| |□□□□| Undefined
Let A = 30 -1 B C = D= find 9 1. A+ 3B 2. B - 2A = 3. CD= 4. DC =
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find A-? using the formula A-1 adj(A). det(A)
Let A = {1, 2}, B = {3, 5, 6}, C = {1, 2, 3, 5, 7}, D = {4, 7, 9}, and U = {1, 2, 3, . . . , 9, 10}. 1. Find B ∪ C. 2. Find B ∩ C. 3. Find A ∪ B. 4. Find C ∩ D. 5. Find C'. 6. Find B'. 7. Is 4 ∈ C? 8. Is B ⊆ C? 9. Is A ⊆ C? 10. Are A and B...
Let U be as in question 6. Let D = {1, 3, 5, 7} E = {2, 4, 6, 8} and F = {1, 2, 3}. For the following questions state whether each statement is true or false a.)D and E are disjoint. b.)D and E are complimentary. c.)9 ∈ D d.)D ∩ DC = ∅
(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
three seperate questions multiple choice 13 and B= Find A -B. 2 . [4:1 Let A= -1 6 2 6 7 177 15 12 1 5 5 30 1 5 3 30 7 17 15 36 Let A and B be 3 x 3 matrices with det(A) = 2 and det(B) = -3. Then find det(-A2B). -6 -12 6 12 [5 2 -2 3 -47 0 4 21 _0 Find the determinant of the matrix, A= 10 0 -2 3...