Determine whether each of the following is TRUE (i.e. always true) or FALSE (i.e. not always true...
Determine whether each of the following is Always True, Sometimes True, or Always False. If the statement is Always True or Always False, provide a brief justification. If the statement is Sometimes True, provide an example of a series that makes it true and an example of a series that makes it false. In the following, {a_n}∞n=1 is a sequence and {s_n}∞n=1 refers to the corresponding sequence of partial sums. (a) If lim n→∞ s_n = 0, then lim n→∞...
Determine whether each of the following statements is true or false. In each case, answer true or false, and justify your answer. 3n^2 - 42 = O(n^2) n^2 = O(n log n) 1/n = O(1) n^n = ohm(2^n)
6. (15) Determine whether each statement is true or false. Justify your answers. (a) if f(n) = O(g(n)), then g(n) = O(f(n)). (b) if f(n) = O(g(n)), then g(n) = Ω(f(n)). (c) if f(n) = Θ(g(n)), then g(n) = Θ(f(n)).
3. True or False. Please tell whether each of the following statements is true or false and justify your answer in a few sentences. (a) “Free trade is always good and governments should not manage trade.” (b) “Vertical FDI and trade are substitutes, while horizontal FDI and trade are complements.” (c) An import quota cannot make a country better off. (d) Increasing returns to scale will lead to monopolies in world trade and therefore consumers will lose from trade.
6. Determine whether each of the following is true or false (note: the statement is true if it is always true, otherwise it is false). If you say it is true then refer to a known result or give a proof, while if you say it is false then give a counterexample, i.e., a particular case where it fails. (a) If A, B and C are independent, the Pr(AlBnc)- Pr (A) (b) The events S., A are independent (S is...
Determine whether each statement is True or False. Justify each answer a. A vector is any element of a vector space. Is this statement true or false? O A. False; a vector space is any element of a vector O B. True by the definition of a vector space O C. False; not all vectors are elements of a vector space. b. If u is a vector in a vector space V, then (-1)u is the same as the negative...
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
For each of the following statements, determine whether it is true or false and explain why: (a) If ?(?) = ?(?) ∗ h(?), then ?(? − 1) = ?(? − 1) ∗ h(? − 1). (b) If y(t) = x(t) ∗ h(t), then y(−t) = x(−t) ∗ h(−t). (c)If x(t)=0 for t >T1 and h(?)=0 for ? >?2 , then ?(?)∗h(?)=0 for ? > ?1 + ?2
1. Let A be an m x n matrix. Determine whether each of the following are TRUE always or FALSE sometimes. If TRUE explain why. If FALSE give an example where it fails. (a) If m n there is at most one solution to Ax = b. always solve Ax b (b) If n > m you can (c) If n > m the null space of A has dimension greater than zero. (d) If n< m then for some...