Problem 1. We denote by (2 the set of all sequences u = (uk)k=1,2,. = (u1, u2, ...) (uk EC) satisfying luk| < oo. We define the inner product of as follows: k=1 (u, v) = uTE (u, v e l). k=1 Then, e is a Hilbert space. From the following choices, please choose orthonormal systems of (e. (1) {(1,0,0,0, ..), (0, 1, 0,0, ...), (0, 0, 1,0,.)}. (2) {(1,0,0,0, 0, ..), (0, 2,0, 0, 0, .), (0,0, 3, 0,0, ..), (0,0,0, 4, 0, ...),.}. 1 0,0,0,0,. /2' 1 0, V2 1 =,0,0,0, V2 1 0,0, --). 1 (3) , 0,0, .... (0,0.0 1 1 0, (4) {( 1 ,0,0,0,0, .. 1 ,0,0,0,0, .... 2 V2 1 1 1 ,0,0,... %3B 1 0,0,... V2' V2 -) (a, 1 ,0, | /2

Problem 1. We denote by (2 the set of all sequences u = (uk)k=1,2,. = (u1, u2, ...) (uk EC) satisfying luk| < oo. We define the inner product of as follows: k=1 (u, v) = uTE (u, v e l). k=1 Then, e is a Hilbert space. From the following choices, please choose orthonormal systems of (e. (1) {(1,0,0,0, ..), (0, 1, 0,0, ...), (0, 0, 1,0,.)}. (2) {(1,0,0,0, 0, ..), (0, 2,0, 0, 0, .), (0,0, 3, 0,0, ..), (0,0,0, 4, 0, ...),.}. 1 0,0,0,0,. /2' 1 0, V2 1 =,0,0,0, V2 1 0,0, --). 1 (3) , 0,0, .... (0,0.0 1 1 0, (4) {( 1 ,0,0,0,0, .. 1 ,0,0,0,0, .... 2 V2 1 1 1 ,0,0,... %3B 1 0,0,... V2' V2 -) (a, 1 ,0, | /2

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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