Exercise 1. Let 0 < & ≤ 1, and A := [10] E (i) Calculate the condition number of A in the 1-, 2- and ∞-norms. (ii) How do the condition numbers behave as → 0? Why is this the case
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- 1- show that [Am,A"] = 0 for all m and n discuss the physical meanings of this relation. 2- Evaluation the commutation relation [x](a) Determine whether the relation ~ on C with 2₁ ~ 22 iff 21 = Z2 is reflexive, whether it is symmetric, and whether it is transitive. Prove your answers.1. Show that which of these relations on the set of all functions on Z→Z are equivalence relations? (a) R = {(S,8)|S (1) –g(1)} (b) R = {(f,g)|f (0) = g (0) or f(1)=g(1)}
- Q.No.2 a. Show that by using Laws that if the compound statement is logically equal. [ p ^ ( ~ ( ~p V q) ) ] V (p^q) = p b. A function g: Z → Z is defined by the rule g(m,n) = m +n Determine whether it is onto or not... c. Let X= {p, q, r, s, t}, Y= {1, 23} and Z={k, e} Define one-to-one function and how many one-to-one function are there from Y to X Define onto function and how many onto function are there from Y to Z.Exercise 3. Are the following subsets of the real line with its usual topology (in which U CR is open if and only if for every x ‹ U there is € > 0 with (x − €, x + € ) ≤ U) open, closed, both or neither? Explain. (1) [1,3); (2) (1,3) U (5,00); (3) (-∞0, ∞0); (4) { neN} U {0}; (5) The set Q of rationals. .Please help. I am having trouble understanding what to do for these questions. Please show your work Thank you
- 6.3) If f = u + iv is non-constant and analytic in an open set U, which one of the following are analytic as well? (a) g = u - iv, (b) h = v +iu, (c) k = -u -iv, (d) l= iu - v.(iii) The outer measure is translation invariant i.e. for every set A and for each x = R, m* (A + x) = m* (A).1. Let S = (0,7) U 27 +13... Define < on S by a13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all positive integers greate than or equal to 2. Define a function T:S → D as follows: For each integer n ≥ 2, T(n) = the set of all even factors of n. a) Find T(10). b) Find T(17) c) Find T(m), where m is any odd positive integer.1. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1spPlease help. I am having trouble understanding what to do for these questions. Please show your work Thank youRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,