Compute the following determinants:
L2 6 3] -2 2 ( b + c ) _ a 4. Compute the following determinants: 1 2 0 0 0 2 2 3 0 0 6 0 4 3 2 0 0 0 511ー3.0 0.0 () at up
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
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...
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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.
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
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
Compute each of the following matrix multiplications or say why it is impossible. 1 2[2 3 1-3 4 0 4 1 3 -1 6 (iii) [0-33][2 33] 0 4 34 1 2
Compute each of the following matrix multiplications or say why it is impossible. 1 2[2 3 1-3 4 0 4 1 3 -1 6 (iii) [0-33][2 33] 0 4 34 1 2
Determine which property of determinants the equation illustrates. 1 3 2 0 0 0 96 -8 = 0 If one row of a matrix is a multiple of another row, then the determinant of the matrix is zero. If one row of a matrix consists entirely of zeros, then the determinant of the matrix is zero. If two columns of a matrix are interchanged, then the determinant of the matrix changes sign. If a row of a matrix is multiplied...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
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)')