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Let e = (1, 0, 0), e2 = (0, 1, 0) and ez = (0, 0, 1), and let V span(e1, e2) and W = span(e1 + e2 + e3) Which one of the following statements is true? V O W = R³ but V W a. L m 3 but I

Let e = (1, 0, 0), e2 = (0, 1, 0) and ez = (0, 0, 1), and let V span(e1, e2) and W = span(e1 + e2 + e3) Which one of the following statements is true? V O W = R³ but V W a. L m 3 but I

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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Let ej = (1, 0, 0), e2 = (0, 1, 0) and ez (0, 0, 1), and let V = span(e1, e2) and W = span(e1 + e2 + e3) Which one of the following statements is true? a. V O W = R³ but V W b. V + W R’ but V 1 W V + W # R' and V W С. O d. The sum of V and W is not a direct sum, but V + W = R’and V IW 3 V O W = R' and V I W е. O f. The sum of V and W is not a direct sum, but V + W = R’andV ĮW.
Transcribed Image Text:Let ej = (1, 0, 0), e2 = (0, 1, 0) and ez (0, 0, 1), and let V = span(e1, e2) and W = span(e1 + e2 + e3) Which one of the following statements is true? a. V O W = R³ but V W b. V + W R’ but V 1 W V + W # R' and V W С. O d. The sum of V and W is not a direct sum, but V + W = R’and V IW 3 V O W = R' and V I W е. O f. The sum of V and W is not a direct sum, but V + W = R’andV ĮW.
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