Consider the following 3 permutations in S10:σ=1 2 3 4 561 4 5 6 8 10789 107 9 2 3μl =T =12 32 5 1012 3 4 5 6 7 8 9 1010 9 8 4 3 2 1 5 674 54 96 7 8 9 103 8761Jompute τμ-1σ.Express μ as a product of disjoint cycles and then as a product of transpositions.Find the smallest value of n so that " = i, where i is the identity permutation.Find ¹00

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Answered: Consider the following 3 permutations…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Find an explicit formula for the nth term for an, given the following recursive relation: an = 2an-1+ 15an-2, a, = 4, a, = 0
Let A = 1. if ATX B = m = -2 -1 m n 1 -5 n = 3 0 and B= 1 -2 6 -2 5 -35 14 - 12 find mand ni (BTA)? 2. Is it possible to multiply BT by A (BTXA)?
4. tank contains 200 liters of fluid in which 30 grams of salt are dissolved. Brine containing 2 grams of salt per liter is then pumped into the tank at a rate of 4 L/min . The well mixed solution is pumped out at a faster rate of 5L/ min. Set up an initial value problem (a differential equation with an initial condition) to find the amount of salt Q(t) in the tank at any time t. (Do not solve the equation).
Please do Exercise 14.4.21 part B and D. Please show step by step
Question 11 Let gcd(66,255) =d and there exist r,s € Z such that 255r+66s=d. Pick the correct value of r,s and d. Or= -7, s27 and d = 3 Or 7, s= 27 and d = 3 O r = 7, s= -27 and d = 3 Or=-7, s= -27 and d = 3 Question 12 Compute 139112 mod 27. (Use Euler theorem) 11 O 12 13 4 Question 13 Find the inverse of 49 modulo 53 O 11 12 O 13 10 O 14 11.
Obtain the generating function for the number of k-part compositions of n in which the ith part does not exceed 5i for all i = 1, 2, ... , k.
Compute the indicated products involving the following permutations of S, : 1 2 3 4 5 2 35 4 1 1 2 3 4 5 o = T = 3 54 1 2 (а) то (b) 7°o (c) o-l7 (d) o-27 (Note: µ-" = ()" for any natural number n and any permutation
excercise 4.1 #2
excercise 4.1 #4
The cofactor C.;; of the entry a¡¡ is given by (-1)³ + İM¡¡. Substitute this expression in the cofactor expansion. Cij 87-6 1 -2 0 7 0 6 7 8 5 0 6 -3 -6 = 87-6 1 -20 7 0 6 7 8 5 0 6 -3 -6 1M 21 |(−1)² + ¹M ₂1 = + + |(−1)² + 2M 22- 7 -6 1 (-1) 7 8 5 6 -3 -6 (−1)² + ³M 23 The minor M,; of the entry a¡;; is the determinant of the matrix obtained by deleting the ith row and jth column. Use this fact to write the minors in the expansion. Remember that an even power of -1 is ij 1 and an odd power of -1 is -1. + + 87 1 (-1) 6 7 5 06-6 (-1)² + AM 24
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