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A counter-example is an example which shows that a proposed theorem (conjecture) is false. For example, p = 2 is a counter- example to: "If p is prime then p is odd." In this question, we only consider R-vector spaces. Prove or give a counter-example: If {1,..., V} CV is linearly independent and Ô then {\v1,..., Av} is linearly independent.

A counter-example is an example which shows that a proposed theorem (conjecture) is false. For example, p = 2 is a counter- example to: "If p is prime then p is odd." In this question, we only consider R-vector spaces. Prove or give a counter-example: If {1,..., V} CV is linearly independent and Ô then {\v1,..., Av} is linearly independent.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 43E: Prove that in a given vector space V, the zero vector is unique.
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A counter-example is an example which shows that a proposed theorem (conjecture) is false. For example, p = 2 is a counter- example to: "If p is prime then p is odd." In this question, we only consider R-vector spaces. Prove or give a counter-example: If {1,..., V} CV is linearly independent and Ô then {\v1,..., Av} is linearly independent.
Transcribed Image Text:A counter-example is an example which shows that a proposed theorem (conjecture) is false. For example, p = 2 is a counter- example to: "If p is prime then p is odd." In this question, we only consider R-vector spaces. Prove or give a counter-example: If {1,..., V} CV is linearly independent and Ô then {\v1,..., Av} is linearly independent.
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