Let W be the union of the first and third quadrants in the xy-plane. That is, let W = · {[y] :x² + y² ≤ 1}. (a) If u is in W and c is any scalar, is cu in W? Why? (b) Find specific vectors u and v in W such that u+v is not in W. (This is enough to show that W is not a vector space.)
Let W be the union of the first and third quadrants in the xy-plane. That is, let W = · {[y] :x² + y² ≤ 1}. (a) If u is in W and c is any scalar, is cu in W? Why? (b) Find specific vectors u and v in W such that u+v is not in W. (This is enough to show that W is not a vector space.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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