Let V={(x,y)|x,y∈R} with addition and scalar multiplication defined as u+v=(u1+v1−3,u2+v2+1) and ku=(ku1,ku2), respectively, where k is a scalar and u=(u1,u2) and v=(v1,v2). Which of the following is true? A. The zero of V is (0,0) and 1u=u. B. The zero vector in V is (3,−1) and the negative of (2,7) is (4,−9) C. V is a vector space and the zero of V is (3,−1). D. 4[(1,2)+(3,−4)]=4(1,2)+4(3,−4) and addition is associative. E. The negative of (1,2) is (−1,−2) and k(lu)=(kl)u for all u∈V and all scalars k,l.

Let V={(x,y)|x,y∈R} with addition and scalar multiplication defined as u+v=(u1+v1−3,u2+v2+1) and ku=(ku1,ku2), respectively, where k is a scalar and u=(u1,u2) and v=(v1,v2). Which of the following is true? A. The zero of V is (0,0) and 1u=u. B. The zero vector in V is (3,−1) and the negative of (2,7) is (4,−9) C. V is a vector space and the zero of V is (3,−1). D. 4[(1,2)+(3,−4)]=4(1,2)+4(3,−4) and addition is associative. E. The negative of (1,2) is (−1,−2) and k(lu)=(kl)u for all u∈V and all scalars k,l.

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 52E

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