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X Document1 - Word AutoSave evie tucker Off ET Mailings Review Share File Design References View Help Search Home Insert Draw Layout Comments Find Cut 11A A Aa A E2T Calibri (Body) AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A ав Replace Copy Paste Dictate No Spa.... Heading T Normal Heading 2 Title В IUab- х, х* А Select Format Painter Clipboard Paragraph Styles Editing Voice Font N 1 3 1 1 C Col(A) 1. Let A= 2 1 2 1 a) Find an orthonormal basis for C. D. Focus Page 1 of 1 0 words 100% 8:29 PM a Type here to search W 25 12/2/2019 !Tili

X Document1 - Word AutoSave evie tucker Off ET Mailings Review Share File Design References View Help Search Home Insert Draw Layout Comments Find Cut 11A A Aa A E2T Calibri (Body) AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A ав Replace Copy Paste Dictate No Spa.... Heading T Normal Heading 2 Title В IUab- х, х* А Select Format Painter Clipboard Paragraph Styles Editing Voice Font N 1 3 1 1 C Col(A) 1. Let A= 2 1 2 1 a) Find an orthonormal basis for C. D. Focus Page 1 of 1 0 words 100% 8:29 PM a Type here to search W 25 12/2/2019 !Tili

Advanced Engineering Mathematics
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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X Document1 - Word AutoSave evie tucker Off ET Mailings Review Share File Design References View Help Search Home Insert Draw Layout Comments Find Cut 11A A Aa A E2T Calibri (Body) AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A ав Replace Copy Paste Dictate No Spa.... Heading T Normal Heading 2 Title В IUab- х, х* А Select Format Painter Clipboard Paragraph Styles Editing Voice Font N 1 3 1 1 C Col(A) 1. Let A= 2 1 2 1 a) Find an orthonormal basis for C. D. Focus Page 1 of 1 0 words 100% 8:29 PM a Type here to search W 25 12/2/2019 !Tili
Transcribed Image Text:X Document1 - Word AutoSave evie tucker Off ET Mailings Review Share File Design References View Help Search Home Insert Draw Layout Comments Find Cut 11A A Aa A E2T Calibri (Body) AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A ав Replace Copy Paste Dictate No Spa.... Heading T Normal Heading 2 Title В IUab- х, х* А Select Format Painter Clipboard Paragraph Styles Editing Voice Font N 1 3 1 1 C Col(A) 1. Let A= 2 1 2 1 a) Find an orthonormal basis for C. D. Focus Page 1 of 1 0 words 100% 8:29 PM a Type here to search W 25 12/2/2019 !Tili
Expert Solution
Step 1

Covert the matrix into echelon form.

1 3 5 -1 -3 1 A = 2. 1 5 2 8 R, -R - R, R->R, - R 1 R2RR 1 1. 2 2 -3 O 2. 3 3 5 2 3 6 2 -3 2 RR R R, ->R, - R, 1 0 2 0 0 6 0 0 -6 0 0 Row1 and Row2 contains the lea ding entries, hence first and secondcolumn ofthe original matrix forms the basis for column space of A 00 n o en en O O n O O O
Step 2

Basis for Col(A).

1 3 -1 -3 Col (A)=0 2 1 5 1 5
Step 3

Find the orthogonal basis by Gram Schmidt Orthogonalisation process.

Let (1-1,0,1,1 v= (3,-3,2,5,5) be the orthogonal basis. Then by Gram Schmidt's process Let Wi and W (1,-1,0,1,1) -Wi (Mi.Wa ((3,-3,2,5,5).(1.-1,0,1,1) (1-1,0,1,1),(1-1,0,1,1) (3,-3,2,5,5) -(3,-3,2,5,5)-4(1-1,0,1,1) = (-1,1,2,1,1) Hence,1,-1,0,1,1),(-1,1,2,1,1)} is the orthogonal basis.
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