Document1 - Microsoft Word (Product Activation Failed)FileHomeInsertPage LayoutReferencesMailingsReviewViewa ?% CutA Find -- A AE- E - F章 TCalibri (Body)- 11AaAalAaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcLE CopyСopyae ReplaceB I UU - abe x, x²abAI NormalI No Spaci. Heading 1PasteAChange.Heading 2TitleSubtitleWFormat PainterStyles - Select -ClipboardFontParagraphStylesEditingL• 2. 1:.I' 2: 1 : 3:1• 4.I 5.1' 6.1'7I'8: 1 9 ' 10.L· 11: 1 ' 12.'13 · L 14: 1· 15.1A L'17:1 18Problem 32. Suppose e¡, e2, ..., e, is an orthonormal basis of V and v1 , vz, ..., V, are– v;|| <1for each j. Prove that v1, v2, ..., Vn is avectors in V such that ||e;basis of V.all04:42 PM2021-08-18 Page: 1 of 1国昆言E E E E+Words: 0100% -

Answered: Image /qna-images/answer/00dfb2a6-b99d-4577-a920-0b40c550fd09.jpg

Answered: Problem 32. Suppose e1, e2, .., e, is…

Problem 32. Suppose e1, e2, .., e, is an orthonormal basis of V and v1 , vz, .., ",n are for each j. Prove that vi, v2, ..., 'n is a vectors in V such that ||ej – v;|| < basis of V.

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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Document1 - Microsoft Word (Product Activation Failed)
File
Home
Insert
Page Layout
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View
a ?
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A Find -
- A A
E- E - F
章 T
Calibri (Body)
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AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL
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B I U
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Paste
A
Change
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Heading 2
Title
Subtitle
W
Format Painter
Styles - Select -
Clipboard
Font
Paragraph
Styles
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L
• 2. 1:.
I' 2: 1 : 3:1
• 4.I 5.1' 6.1'7
I'8: 1 9 ' 10.L· 11: 1 ' 12.'13 · L 14: 1· 15.1A L'17:1 18
Problem 32. Suppose e¡, e2, ..., e, is an orthonormal basis of V and v1 , vz, ..., V, are
– v;|| <
1
for each j. Prove that v1, v2, ..., Vn is a
vectors in V such that ||e;
basis of V.
all
04:42 PM
2021-08-18 Page: 1 of 1
国昆言
E E E E
+
Words: 0
100% -

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3. Prove the following to establish theorem 7. (a) If the set of vectors {₁, 2, 3, ...} in R" are linearly dependent then at least one of the vectors can be expressed as a linear combination of the others. (b) If at least one of the vectors from the set containing vectors ₁, 2, 3, ... in Rn can be expressed as a linear combination of the others then the vectors form a linearly dependent set.
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: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D