Let ej (1, 0, 0), е2 — (0, 1, 0) and ez (0, 0, 1), and let V = span(e1, e2) and W span(e, + e2 + e3) Which one of the following statements is true? a. V + W # R'and V W O b. The sum of V and W is not a direct sum, but V + W = R'and V W O c. The sum of V and W is not a direct sum, but V + W = R' and V Į W O d. V OW = R' but V W Ое. V өW - R and V I W %3D O f. V + W + R' but V 1 W

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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Let ej =
(1, 0, 0), e2 = (0, 1, 0) and ez
(0, 0, 1), and let
V
span(e1, e2)
and
W =
span(e, + e2 + e3)
Which one of the following statements is true?
V + W # R' and V W
а.
O b. The sum of V and W is not a direct sum, but V + W = R’and V 1 W
С.
The sum of V and W is not a direct sum, but V + W = R´ and V W
d. V O W = R' but V Į W
V O W = R³ and V 1 W
е.
O f. V + W + R´ but V 1 W
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(e, + e2 + e3) Which one of the following statements is true? V + W # R' and V W а. O b. The sum of V and W is not a direct sum, but V + W = R’and V 1 W С. The sum of V and W is not a direct sum, but V + W = R´ and V W d. V O W = R' but V Į W V O W = R³ and V 1 W е. O f. V + W + R´ but V 1 W
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