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Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u. Which of the following statements åre then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector 0 + u, is not equal to u Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + 0 0, which contradicts that u, is an additive identity. O The statement u, +0 0 + u which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, +0 U, which contradicts that O is an additive identity. O The statement u, + 0 0, which contradicts that u, must have an additive inverse. Therefore, the additive identity in a vector space is unique.

Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u. Which of the following statements åre then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector 0 + u, is not equal to u Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + 0 0, which contradicts that u, is an additive identity. O The statement u, +0 0 + u which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, +0 U, which contradicts that O is an additive identity. O The statement u, + 0 0, which contradicts that u, must have an additive inverse. Therefore, the additive identity in a vector space is unique.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u,. Which of the following statements are then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un: O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector o + u, is not equal to u: Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + o 0, which contradicts that u, is an additive identity. O The statement u, +0 # 0 + u, which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, + 0 U, which contradicts that O is an additive identity. O The statement u, + 0 + 0, which contradicts that u, must have an additive inverse. Therefore, the additive identity in a vector space is unique.
Transcribed Image Text:Prove that in a given vector space V, the zero vector is unique. Suppose, by way of contradiction, that there are two distinct additive identities 0 and u,. Which of the following statements are then true about the vectors 0 and u,? (Select all that apply.) O The vector 0 + u, is not equal to u, + 0. O The vector 0 + u, is equal to un: O The vector 0 + u, is not equal to 0. O The vector 0 + u, does not exist in the vector space V. O The vector 0 + u, is equal to 0. O The vector o + u, is not equal to u: Which of the following is a result of the true statements that were chosen and what contradiction then occurs? O The statement u, + o 0, which contradicts that u, is an additive identity. O The statement u, +0 # 0 + u, which contradicts the commutative property. O The statement u, = 0, which contradicts that there are two distinct additive identities. O The statement u, + 0 U, which contradicts that O is an additive identity. O The statement u, + 0 + 0, which contradicts that u, must have an additive inverse. Therefore, the additive identity in a vector space is unique.
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