Question 36 Let V be a real inner product space. Which of the following statements is true? (i) 0 is the only vector in V that is orthogonal to itself. (m) u +w < u+wif and only if one of u and w is a non negative scalar multiple of the other. (1) Ku, w=uw| if and only if one of u and w is a scalar multiple of the other. O B. only (ii) O A. only (i) O D. only (i) and (iii) O E. All the statements. OC. only (iii) A Moving to ancther question will save this response. O Type here to search
Question 36 Let V be a real inner product space. Which of the following statements is true? (i) 0 is the only vector in V that is orthogonal to itself. (m) u +w < u+wif and only if one of u and w is a non negative scalar multiple of the other. (1) Ku, w=uw| if and only if one of u and w is a scalar multiple of the other. O B. only (ii) O A. only (i) O D. only (i) and (iii) O E. All the statements. OC. only (iii) A Moving to ancther question will save this response. O Type here to search
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:Question 36
Let V be a real inner product space. Which of the following statements is true?
(i) O is the only vector in V that is orthogonal to itself.
(ii)
(u+w< u|+w if and only if one of u and w is a non negative scalar multiple of the other.
||+|"| = |m+ n||
if and only if one of u and w is a scalar multiple of the other.
(i) |Ku, w>|=||u||
O B. only (ii)
O A. only (i)
O D. only (i) and (iii)
OE. All the statements.
O C. only (ii)
A Moving to another ouestion will save this response.
Type here to search
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Step 1 proving cauchy schwarz inequality for real inner product space
VIEWStep 2 some calculation to prove the inequality
VIEWStep 3 (4) is the cauchy schwarz inequality then prove triangle property
VIEWStep 4 discussion option (ii) (i) and (iii)
VIEWStep 5 remaining part for option (iii)
VIEWStep 6 some needed calculation
VIEWStep 7 conclusion
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