Find the terms of the determinant associated with the permutations 2,3,1,4 and 3,1,4,2
Compute the determinant?
1 [? ? 0 1 -1 0 3 -1 3 0 ? 0 4 ? Find the terms of the determinant associated with the permutations 2,3,1,4 and 3,1,4,2 Compute the determinant?
Find the terms of the determinant associated with the permutations 2,3,1,4 and 3,1,4,2 Compute the determinant?...
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
Also find the Eigenvalues of B
Problem 2 Compute the determinant of 1 0 0 B - XId, where Id = 10 1 0 C: 0 0 1 B= 1 0 0 2 1 -2 3 2 1
Reduce the following 4x4 determinant to upper triangular form and then find the determinant. 1 0 -1 3 2 2 0 0 1 0 4 -1 0 1 -5 1
Find the determinant of the following matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula: (101) y 01 2 x 1) xy-x
Q= II. Permutations. Consider the following permutations in Sg: 1 2 3 4 5 6 7 8 9 3 1 4 5 9 2 6 8 7 2 7 1 8 4 5 9 3 6 1. Express a and B as products of disjoint cycles. 2. Compute a-108-1 3. Find ord(a) and ord(B). 4. Express a and B as products of transpositions.
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 100 5 3 7 3 - 8 200 0 5 3 1 4 1 0 0 3 7 3 200 8 (Simplify your answer.) 5 3 1 4
2. Consider the permutations a (123)(45) and b (2543) in the symmetric group S (a) Compute the conjugate permutation ca using (i) the definition a-b ab (b) What is the order of a? How many permutations have the same shape as a; that is, (x x x)(x x). (c) What is the subgroup H of all permutations in Ss that commute with the permutation a? d) Using the result of the previous part, or otherwise, find 5 other permutations bi,...
Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7→ n + 1 − i. (c) Show that this initial configuration of the 15 puzzle is not solvable 3 1 15 13 2 8 5 9 12 7 11 4 14 6 10 − (d) Suppose that (i, j) ∈ Sn is a transposition and that i < j. Find an expression (in terms of i and j...
3.2.12 Combine the methods of row reduction and cofactor expansion to compute the determinant. - 1 590 4 24 0 6 6 8 8 5 3 5 4 The determinant is : (Simplify your answer.) Su dia eo Enter your answer in the answer box and then click Check Answer Lions All parts showing Clear All