Consider N and the set
S={x∈{0,...N-1}:gcd(x,N)=1} where k=|S|
For a∈S, we define T={ax(modN):x∈S}. what is
|T|? Answer may include N and k.
Consider N and the set S={x∈{0,...N-1}:gcd(x,N)=1} where k=|S| For a∈S, we define T={ax(modN):x∈S}. what is |T|? Answer may include N and k.
consider the system X(t) = ax(1) + bu(t) with a = 0.001,b= 1,x(0) = 5. (a) Simulate this system using the Matlab command initial (b) Now use u(t) = -kx(t) where k is found as the optimal gain by minimizing the performance index J= ax (1) + ru (1) dt Use q=1, r=1 to simulate this system.
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
discrete math Search il 17:16 [Problem] 1 (a) Give an external definition of the set S {sls EZA+ and gcd(x, 12) 1) (B) Write all the proper subsets of the set {1, 2 3}, and (c) define the function for real number a and positive integer n ,f: RxZ^+ R as f (a,n) a^n , Give a recursive definition of the function (d) Calculate gcd (60, 22) using Euclidean algorithm (e) Give 3 positive integer x that satisfies 4x 6...
Let Zn* = {x| 1≤x ≤ n-1, where GCD(x, n)=1 }. What are the elements of Z16*?
x(0) = 0 Consider the system defined by * = AX + Bu Where 1 A = (-6-3) BEG 1 and u=C)=6:10 [2.1(t) (5.1(t). Obtain the response x(t) analytically.
1. For n-pg, where p and q are distinct odd primes, define (p-1)(q-1) λ(n) gcd(-1-1.411) Suppose that we modify the RSA cryptosystem by requiring that ed 1 mod X(n). a. Prove that encryption and decryption are still inverse operations in this modified cryptosystem. RSA cryptosystem.
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
, A is a linear transformation that maps vectors x in 975 into vectors Let A= 0 -2 1 b in R2 Consider the set of all possible vectors b-Ax, where x is of unit length. What is the longest vector b in this set, and what unit length vector x is used to obtain it? You can use Matlab to save time with the computations, but please justify your answer. , A is a linear transformation that maps vectors...
Im wondering how to do b). (6) We define the set of compactly supported sequences by qo = {(zn} : there exists some N > 0 so that Zn = 0 for all n >N). We define the set of compactly supported rational sequences by A={(za) E ao : zn E Q for all n E N). (a) Prove that A is countable (b) Prove that for 1 S p<oo the set A is dense in P. You may use...
(2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact. (b) Prove that for any є > 0 there exists some N > 0 so that for any x E A we have (c) Prove that A is totally bounded. (d) Prove that A is compact (2) Define the set A C 2 by s) n-0 (a) Prove that for any N 2 0 the set is compact....