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.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 14E

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Question

Let W be the union of the first and third quadrants in the xy-plane. That is, let W = = {[✓] : 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.)

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