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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Let a subset W be the set of all vectors in R² such that |×₁ | = |x₂|- Apply the theorem for conditions for a subspace to
determine whether or not W is a subspace of R².
According to the theorem of conditions for a subspace, the nonempty subset W of the vector space V is a subspace of V if
and only if it satisfies the following two conditions:
(i) If u and v are vectors in W, then u + v is also in W.
(ii) If u is in W and c is a scalar, then the vector cu is also in W.
Select the correct choice below.
O A. W is a subspace of R2 because it satisfies both of the conditions.
B. W is not a subspace of R² because both conditions (i) and (ii) fail.
C. W is not a subspace of R² because condition (ii) fails while condition (i) is satisfied.
D. W is not a subspace of R2 because condition (i) fails while condition (ii) is satisfied.
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