XDocument1 - WordAutoSaveevie tuckerOffETMailingsReviewShareFileDesignReferencesViewHelpSearchHomeInsertDrawLayoutCommentsFindCut11A A Aa AE2TCalibri (Body)AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A авReplaceCopyPasteDictateNo Spa.... HeadingT NormalHeading 2TitleВ IUab- х, х* АSelectFormat PainterClipboardParagraphStylesEditingVoiceFontN1311C Col(A)1. Let A=2121b) Find a QR factorization for AD. FocusPage 1 of 10 words100%8:31 PMaType here to searchW2512/2/2019

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Asked Dec 3, 2019
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11A A Aa A
E2T
Calibri (Body)
AаBЬСcDc AaBЬСcDc AaBbC AаBbСcL A ав
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Paste
Dictate
No Spa.... Heading
T Normal
Heading 2
Title
В IUab- х, х* А
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Format Painter
Clipboard
Paragraph
Styles
Editing
Voice
Font
N
1
3
1
1
C Col(A)
1. Let A=
2
1
2
1
b) Find a QR factorization for A
D. Focus
Page 1 of 1
0 words
100%
8:31 PM
a
Type here to search
W
25
12/2/2019
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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 b) Find a QR factorization for A D. Focus Page 1 of 1 0 words 100% 8:31 PM a Type here to search W 25 12/2/2019

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Expert Answer

Step 1

We need to find the QR factorization for A.

A 0
1
1
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A 0 1 1

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Step 2

Note:

QR Decomposition with Gram-Schmidt:
= [aj | a2 | a3 |... an],
If A
u1
then u = a, ei
иz — а2 — (а2.e, )ej, ez —
(ак+1:е)е,
l12||
uk+1
(ak+1.ek)e, ek+1 =
(a+1.e2)e2
(ak+1. e1)e
= ak+1
l4+1||
uk+1
Note that is the L2 norm and (a b) = a7b
The resulting QR factorization is
а, е
а,е, а,е,
0
а,е,
QR
A [a1 a2a3| ... | an] = [e | e2 | eg |... | en]
а,ел
0
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QR Decomposition with Gram-Schmidt: = [aj | a2 | a3 |... an], If A u1 then u = a, ei иz — а2 — (а2.e, )ej, ez — (ак+1:е)е, l12|| uk+1 (ak+1.ek)e, ek+1 = (a+1.e2)e2 (ak+1. e1)e = ak+1 l4+1|| uk+1 Note that is the L2 norm and (a b) = a7b The resulting QR factorization is а, е а,е, а,е, 0 а,е, QR A [a1 a2a3| ... | an] = [e | e2 | eg |... | en] а,ел 0

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Step 3

Here,

...
-1
14= Y)? + (-1)? + (0) + (1) + (1) = \4 = 2.
and 14||= (1)? +(-1)? +(0)2 +(1)2 +(1)
a 0
1
1
2
1
1
-1
1
0
1242
2
0
e1
1
2
1
1
2
N |
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-1 14= Y)? + (-1)? + (0) + (1) + (1) = \4 = 2. and 14||= (1)? +(-1)? +(0)2 +(1)2 +(1) a 0 1 1 2 1 1 -1 1 0 1242 2 0 e1 1 2 1 1 2 N |

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Advanced Math