% index vectors for rows and columns
p = 1:m;
q = 1:n;
% index matrices for rows and columns
[P, Q] = ndgrid(p, q);
% create a matrix with the shift values
K = repmat(k(:), [1 n]);
% update the matrix with the column indexes
Q = 1 + mod(Q+K, n);
% create matrix of linear indexes
ind = sub2ind([m n], P, Q);
% finally, create the output matrix
B = A(ind);
Help please! Using matlab Prove or give a counterexample: if f: X rightarrow Y and g:...
Let f : A rightarrow D and g : B rightarrow C be functions. For each part, if the answer is yes, then prove it, otherwise give a counterexample. Suppose f is one-to-one (injective) and g is onto (surjective). Is go f one-to-one (injective)? Suppose f is one-to-one (injective) and g is onto (surjective). Is g f onto (surjective)? Suppose g is one-to one. Is g one-to-one? Suppose g f onto. Is g onto?
Prove or find a counterexample for the following. Assume that f (n) and g (n) are monotonically increasing functions that are always larger than 1. f (n) = o (g (n)) rightarrow log (f (n)) = o (log (g (n))) f (n) = O (g (n)) rightarrow log (f (n)) = O (log (g (n))) f (n) = o (g (n)) rightarrow 2^f (n) = o (2^g (n)) f (n) = O (g (n)) rightarrow 2^f (n) = O (2^g...
please help with matlab Write a MATLAB function with header [y] = mySplit(f,g,a,b,x), where fand g are handles to functions f(x) and g(x), respectively. The output argument from this function y should be: ( f(x) g(x) ( f(x) * g(x) if if y = b<x sa a < x otherwise Hint: • a, b are integer numbers with a > b. • f(x) = x*sin(x) • g(x) = cos(x)/(x²+1)
Suppose that all solutions of the differential equation f(x,y), y = g(x,y) exist for all time and that f and g are smooth (Co) functions. Let 7(t) be the solution of the initial value problem with γ(0) = (1,2). Prove or give a counterexample to the statement that the w-limit set of γ can contain more than one critical point. Suppose that all solutions of the differential equation f(x,y), y = g(x,y) exist for all time and that f and...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y). Determine whether the statement is true or false. If false, explain...
1 Prove the following using the definitions of the notations, or disprove with a specific counterexample: Theta(g(n)) = O(g(n)) Ohm(g(n)) Theta(alpha g(n) = Theta(g(n)), alpha > 0 If f(n) O(g(n)), then g(n) Ohm(f(n)). For any two non-negative functions f(n) and g(n), either f(n) Ohm(g(n)), or f(n) < O(g(n))
how do u do 6? F-'(C-D)= F-'(C)-F-'(D). 4. (10 points) In following questions a function f is defined on a set of real numbers. Determine whether or not f is one-to-one and justify your answers. (a) f(x) = **!, for all real numbers x #0 (6) f(x) = x, for all real numbers x (c) f(x) = 3x=!, for all real numbers x 70 (d) f(x) = **, for all real numbers x 1 (e) f(x) = for all real...
Please solve all parts in this problem neatly 3. Let f(x, y, ). g(y,z) and h(x,y,z) be C2 scalar functions. Prove the following identity: (a) By direct calculation (without using the vector identities) ( b) Using the vector identities. Clearly state which identities you have used . 3. Let f(x, y, ). g(y,z) and h(x,y,z) be C2 scalar functions. Prove the following identity: (a) By direct calculation (without using the vector identities) ( b) Using the vector identities. Clearly state...
Let a function f be f: R rightarrow R such that f(x) = 0 when x lessthanorequalto 0 and f(x) = log(x) * sin(x) when x > 0. f is plotted in the figure below. a) Determine whether f is one-to-one. b) Determine whether f is onto. c) Determine whether f is total. d) Determine ranges for x and y so that f is total but not one-to-one. e) Determine ranges for x and y so that f is one-to-one,...
1. Prove that the function f: X → Y is injective if and only if it satisfies the following condition: For any set T and functions g: T → X and h : T → X, o g = f o h implies g = h.