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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.)

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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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