Let V be a vector space over R. Prove that if a E R and T E V satisfy au = 0, then a = 0 or = 0. (Make sure you use the axioms of vector spaces. Hint: what do you know about a real number a if a + 0? You may wish to use the previous problem.)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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0. then a =
0 or i = 0.
Let V be a vector space over R. Prove that if a E R and v E V satisfy au
(Make sure you use the axioms of vector spaces. Hint: what do you know about a real number a if
a + 0? You may wish to use the previous problem.)
Transcribed Image Text:0. then a = 0 or i = 0. Let V be a vector space over R. Prove that if a E R and v E V satisfy au (Make sure you use the axioms of vector spaces. Hint: what do you know about a real number a if a + 0? You may wish to use the previous problem.)
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