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LINEAR ALGEBRA PLEASE ANSWER ALL QUESTIONS Let fa, fo, fe € P2(A) denote the Lagrange polynomials associated with the distinct real numbers a, b, c respectively, and let V = span{f,+f, o+te} and W = span{f,a+fs+fc}. Let T : P2(R) → P2(R) be the projection on V along W, and let g eE P2(R). .1 Show that 3 = {f, + fe, fo + fo, fa + fo + fo} is linearly independent. 2 Show that Pa(R) = V@ W. 3 Find a formula formula for T(g) expressed as a linear combination of {fa, fo, fe}.

LINEAR ALGEBRA PLEASE ANSWER ALL QUESTIONS Let fa, fo, fe € P2(A) denote the Lagrange polynomials associated with the distinct real numbers a, b, c respectively, and let V = span{f,+f, o+te} and W = span{f,a+fs+fc}. Let T : P2(R) → P2(R) be the projection on V along W, and let g eE P2(R). .1 Show that 3 = {f, + fe, fo + fo, fa + fo + fo} is linearly independent. 2 Show that Pa(R) = V@ W. 3 Find a formula formula for T(g) expressed as a linear combination of {fa, fo, fe}.

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 ? % Cut A Find - - =。三,年 外T Calibri (Body) - 11 A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace Paste BI U abe x, x* A ab A I Normal I No Spaci. Heading 1 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 ANSWER ALL QUESTIONS Let fa, fp, fe € P2(R) denote the Lagrange polynomials associated with the distinct real numbers a, b, c respectively, and let V = span{fa+fe, fz+fc} and W = span{fa+f3+fc}. Let T : P2(R) → P2(R) be the projection on V along W, and let g e P2(R). .1 Show that 3 = {fa + fe, fo + fo, fa + fo + fo} is linearly independent. 2 Show that Pe(R) = Ve W. 3 Find a formula formula for T(g) expressed as a linear combination of {fa, fo, fe}. 06:40 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - +)
Transcribed Image Text:W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - - =。三,年 外T Calibri (Body) - 11 A A Aa Aal AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace Paste BI U abe x, x* A ab A I Normal I No Spaci. Heading 1 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 ANSWER ALL QUESTIONS Let fa, fp, fe € P2(R) denote the Lagrange polynomials associated with the distinct real numbers a, b, c respectively, and let V = span{fa+fe, fz+fc} and W = span{fa+f3+fc}. Let T : P2(R) → P2(R) be the projection on V along W, and let g e P2(R). .1 Show that 3 = {fa + fe, fo + fo, fa + fo + fo} is linearly independent. 2 Show that Pe(R) = Ve W. 3 Find a formula formula for T(g) expressed as a linear combination of {fa, fo, fe}. 06:40 PM 2022-05-10 Page: 1 of 1 Words: 6 E EA E E E 100% - +)
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