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Let T : R" → R™ be a linear transformation, and let {V₁, V2, №3} be a linearly dependent set in Rn. Prove the following statement. Your work should be legible, and all your logic should be clear and justified. The set {T(v₁), T(v₂), T(73) } is linearly dependent.

Let T : R" → R™ be a linear transformation, and let {V₁, V2, №3} be a linearly dependent set in Rn. Prove the following statement. Your work should be legible, and all your logic should be clear and justified. The set {T(v₁), T(v₂), T(73) } is linearly dependent.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 22CR: Let T be a linear transformation from R2 into R2 such that T(1,1)=(2,3) and T(0,2)=(0,8). Find...
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Let T : R” → R™ be a linear transformation, and let {V₁, V2, V3} be a linearly dependent set in R”. Prove the following statement. Your work should be legible, and all your logic should be clear and justified. The set {T(v₁), T(v₂), T(√3) } is linearly dependent.
Transcribed Image Text:Let T : R” → R™ be a linear transformation, and let {V₁, V2, V3} be a linearly dependent set in R”. Prove the following statement. Your work should be legible, and all your logic should be clear and justified. The set {T(v₁), T(v₂), T(√3) } is linearly dependent.
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