Suppose T V W is a one-to-one linear transformation. Carefully show that if 77 (v₁) + 3T (₂) - T (v3) = 0w then 7v₁ + 3v₂ = V3. Verify/justify each step (tha use linearity, one-to-one, etc., state when and where).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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Suppose T: V→ W is a one-to-one linear transformation. Carefully show that if
7T (v₁) + 3T (v₂) - T (v3) = 0w then 7v₁ + 3v₂ = V3. Verify/justify each step (that is
use linearity, one-to-one, etc., state when and where).
Transcribed Image Text:Suppose T: V→ W is a one-to-one linear transformation. Carefully show that if 7T (v₁) + 3T (v₂) - T (v3) = 0w then 7v₁ + 3v₂ = V3. Verify/justify each step (that is use linearity, one-to-one, etc., state when and where).
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