Give 3 different examples of norms on R
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Q: Give 3 different examples of norms on Z (set of integers)
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Q: a) ||x|| = (x1)² + (x2)² (Euclidian norm) b) ||x|| = (x1)² + 5(x2)² c) ||x|| = |x4| + |x2|
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Q: 3. A = {2, 2+2, 2+4,2+6, 2+8} where A = {2,4,6,8} 4. A=(1-22, 1+22) where A = Z*
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Q: 3. For any p.q21 prove that || - ||, and || - || define two equivalent norms on IR".
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- 3) Let the order on the Xe(-002)Q be the Knoun order. find the Sapremum Supremum andinfimum of the setLet n, k EN and define the family of graphs G (V, Ek) on the vertex set V,= (1,2,... ,n} and with edge set Enk= {(i,j) EV, x V: i j (mod k)}. In other words, two vertices i and j are adjacent if they are congruent modulok. (a) Draw G42 and G73 and show they are both disconnected. (b) Show that G is connected if and only if k= 1. (c) Show that Gis the empty graph if and only if n1. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1sp3. Two normg 11·11 and Ill·lll on а vector Space X are equivalent if there exists спо 070 such that _ |||X| || = ||X|| = (111 all!, xf X 드 XThe following are true about the Alternativehypothesis, except. A) A hypothesis that the investigator is trying to prove B)Investigator's Hypothesis C)A hypothesis that the investigator is trying to reject D) There is a true relationship between variablesRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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