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3. For both proofs in this problem, you may not write or refer to any of the entries of any vector. (Hint: Use only the properties from §2.1 Theorem 1 from the lecture notes.) (a) Let a € Rn be a vector satisfying b + a = b for all b € R". Prove that a = 0. (b) Let x = R", and let y € R" be such that x +y = 0. Prove that y = -x.

3. For both proofs in this problem, you may not write or refer to any of the entries of any vector. (Hint: Use only the properties from §2.1 Theorem 1 from the lecture notes.) (a) Let a € Rn be a vector satisfying b + a = b for all b € R". Prove that a = 0. (b) Let x = R", and let y € R" be such that x +y = 0. Prove that y = -x.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
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3. For both proofs in this problem, you may not write or refer to any of the entries of any vector. (Hint: Use only the properties from §2.1 Theorem 1 from the lecture notes.) (a) Let a € Rn be a vector satisfying b + a = b for all b € R". Prove that a = 0. (b) Let x = R", and let y € R" be such that x +y = 0. Prove that y = -x.
Transcribed Image Text:3. For both proofs in this problem, you may not write or refer to any of the entries of any vector. (Hint: Use only the properties from §2.1 Theorem 1 from the lecture notes.) (a) Let a € Rn be a vector satisfying b + a = b for all b € R". Prove that a = 0. (b) Let x = R", and let y € R" be such that x +y = 0. Prove that y = -x.
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