Q3/ Choose the correct answer a, b, c, or d. 1) The compactness of a subset V of a normed space F is (a)Sufficient and necessary condition (b) Necessary condition (c) Sufficient condition (d) all of them true, to existences of the best approximation. 2) Let F = R? and V = ((x,y): (x- 2)2 +y 2 9), for f = (2,0) and || || = I| I, then the best approximation for f from V is (a) x + y 3 (b) (x-2)2 + y 9 (c) (x-1)2 +y2 = 3 (d) (x - 1)2 + y? >9. 3) If E has a strictly convex norm, then for any subspace B of E and any points ge E, there exists (a) one best approximation (b) two best approximation (c) infinity best approximation (d) no answer. 4) A subset A of a vector space V is said to be convex if for any x,y e A, we have ux + (1-)y E A, for each (a) 0 SuS1 (b) 0
Q3/ Choose the correct answer a, b, c, or d. 1) The compactness of a subset V of a normed space F is (a)Sufficient and necessary condition (b) Necessary condition (c) Sufficient condition (d) all of them true, to existences of the best approximation. 2) Let F = R? and V = ((x,y): (x- 2)2 +y 2 9), for f = (2,0) and || || = I| I, then the best approximation for f from V is (a) x + y 3 (b) (x-2)2 + y 9 (c) (x-1)2 +y2 = 3 (d) (x - 1)2 + y? >9. 3) If E has a strictly convex norm, then for any subspace B of E and any points ge E, there exists (a) one best approximation (b) two best approximation (c) infinity best approximation (d) no answer. 4) A subset A of a vector space V is said to be convex if for any x,y e A, we have ux + (1-)y E A, for each (a) 0 SuS1 (b) 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q3/ Choose the correct answer a, b, c, or d.
1) The compactness of a subset V of a normed space F is
(a) Sufficient and necessary condition (b) Necessary condition (e) Sufficient
condition (d) all of them true, to existences of the best approximation.
2) Let F = R? and V ((x,y): (x- 2) + y? 2 9), for f = (2,0) and || | =
II , then the best approximation for f from V is
(a) x + y? 3 (b) (x- 2) + y? 9 (c) (x- 1)2 +y? 3
(d) (x - 1)2 + y?> 9.
3) If E has a strictly convex norm, then for any subspace B of E and any points
ge E, there exists (a) one best approximation (b) two best approximation
(c) infinity best approximation (d) no answer.
4) A subset A of a vector space V is said to be convex if for any x,y E
A, we have ux+ (1- )y E A, for each (a) 0 Sus1 (b) 0 < u <1
'I5>0 (P) I>n50 (0)
5) Every normed space is (a) metric space (b) vector space (c) a and b (d) not
any one of them.
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