Compute the following determinants:
4. Compute the following determinants: 230 0 6 0 3 2 0 4 0 0 (a) b b a b 5 -3 0 0 0 0 6 0 6 0 0 0
1. Evaluate the following determinants: 8 7 3 4 0 2 (a) 4 0 1 (c) 6 0 3 6 03 8 2 3 ab (e) b c с a b 1 1 1 2 3 (b) 4 7 5 3 6 9 4 -2 (d) 8 11 4 х (f) 3 9 5 0 y 2 -18 7
Find determinants of the following matrices: 1 5 7 -1 3 2 A= 3 2 8 B= 6 -2 3 C= 6 1 9 7 10 0 13 4 1 0 4 1 -7 2 3 -4 3 D= 4 12 -3 -9 2 6 7 8
please provide detailed and clear solutions for the following 2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
117 6) Compute the values of determinants using the cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 6) A= 3 4 5 -2 0 10 0 8 10 0 6 3 0 0 15 1 8 - 4 0 0 0 1 0 3 0 0 0 0 1 2 0 0 0 0 0 -9 Answer: det(A)=-3240.
с 1 0 3. Use determinants to find which real values of c make the matrix 0 2c invertible. -1 c1 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. --2 1 2 (b) 2 6 -6 3 3 2 2
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)')
a, b, cL1 {A, ba, c, aab}, L2 = {ca, b}, and L3 {A,abb} Let E 1. (4 pts) Compute L3 L 2. (6 pts) Which of the statements below are TRUE? a) aabaab E b) L L c) саabba E L4
ECS423U (2019) Page 3 Question 2 (Determinants and Vector Spaces) a) Consider the following system of linear equations: kx + y +z= 1 I + y + 1 x + y + 1 Use determinants to find those values of k for which the system has: 1) A unique solution 24 iv) More than one solution v) No solution HINT. solving the determinant equation, please use a trick: just add and substract [15 marks] b) Consider the following matrix: 1...
mixture 3. Let 0 0 1 0 1 2 1 2 Z loo 4 X 0 A= and B = Y 4 1 (a) Compute the determinants of the following matrices: A, B, AB, 5AB, and (AB) (b) Compute the inverse of A. X = 3 Y = 3 Z = 6