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AR ALGEBRA SE ANSWER ALL QUESTIONS T:V → V be a linear operator on a finite-dimensional vector space V over C such that T2 = T. Show that R(T) C N(T – I) and R(T – ) C N(T). 2 Show that V = R(T) + R(T – I).

AR ALGEBRA SE ANSWER ALL QUESTIONS T:V → V be a linear operator on a finite-dimensional vector space V over C such that T2 = T. Show that R(T) C N(T – I) and R(T – ) C N(T). 2 Show that V = R(T) + R(T – I).

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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W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? A Find - A % Cut - =。三,年 外T Calibri (Body) - 11 A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace BI U ab A I Normal I No Spaci. Heading 1 Paste abe x, x* A Change . Heading 2 Title Subtitle W Format Painter Styles - Select - Clipboard Font Paragraph Styles Editing • 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 LINEAR ALGEBRA PLEASE ANSWwER ALL QUESTIONS Let T:V → V be a linear operator on a finite-dimensional vector space V over C such that T² = T. .1 Show that R(T) C N(T – I) and R(T – I) C N(T). 2 Show that V- R(T) + R(T – I). 3 Show that V = N(T) ® N(T – I). %3D 4 Show that T is diagonalisable. 06:43 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - + 2' ! '11· | '10·L • 9
Transcribed Image Text:W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? A Find - A % Cut - =。三,年 外T Calibri (Body) - 11 A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace BI U ab A I Normal I No Spaci. Heading 1 Paste abe x, x* A Change . Heading 2 Title Subtitle W Format Painter Styles - Select - Clipboard Font Paragraph Styles Editing • 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 LINEAR ALGEBRA PLEASE ANSWwER ALL QUESTIONS Let T:V → V be a linear operator on a finite-dimensional vector space V over C such that T² = T. .1 Show that R(T) C N(T – I) and R(T – I) C N(T). 2 Show that V- R(T) + R(T – I). 3 Show that V = N(T) ® N(T – I). %3D 4 Show that T is diagonalisable. 06:43 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - + 2' ! '11· | '10·L • 9
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