PLEASE ANSWER ALL QUESTIONS Consider the vector space V = C² with scalar multiplication over the real numbers A and let W and U be the subspaces of V defined by W - (z1, z) € V : Z2 - z, + 27,} and U= {(z, z2) e V : Z2 = Z, - Z,). 2.1 Find a basis for WnU. 2.2 Express (z,, z2) € V as (z,, z2) = w + u where w e W and u e U. 2.3 Explain whether V = W @ U.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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LINEAR ALGEBRA
PLEASE ANSWER ALL QUESTIONS
Consider the vector space V = C2 with scalar multiplication over the real numbers R and let W
and U be the subspaces of V defined by
W= {(z1, Z2) € V :Z2 = Z1 +2Z1} and U = {(z1, Z2) e V :Z2 = Z1 - Z1}.
2.1 Find a basis for W n U.
2.2 Express (z,, Z2) e V as (z,, Z2) = W + u where w e W and ue U.
2.3 Explain whether V = W ® U.
06:38 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 - =,年章 ↓ 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 ANSWER ALL QUESTIONS Consider the vector space V = C2 with scalar multiplication over the real numbers R and let W and U be the subspaces of V defined by W= {(z1, Z2) € V :Z2 = Z1 +2Z1} and U = {(z1, Z2) e V :Z2 = Z1 - Z1}. 2.1 Find a basis for W n U. 2.2 Express (z,, Z2) e V as (z,, Z2) = W + u where w e W and ue U. 2.3 Explain whether V = W ® U. 06:38 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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