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X1 Let T: R³ → R² be defined by TX₂ X3 Prove that T is a Linear Transformation. Determine the Matrix of T, i.e., TX = AX. Determine dim(Ker T) and dim(Im T). [x₁ + x₂] -3x3

X1 Let T: R³ → R² be defined by TX₂ X3 Prove that T is a Linear Transformation. Determine the Matrix of T, i.e., TX = AX. Determine dim(Ker T) and dim(Im T). [x₁ + x₂] -3x3

Elementary Linear Algebra (MindTap Course List)
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 16CM
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X₁ 7. Let T: R³ R² be defined by TX₂ X3 = [x₁ + x₂] - 3x3 a) Prove that T is a Linear Transformation. b) Determine the Matrix of T, i.e., TX = AX. c) Determine dim(Ker T) and dim(Im T).
Transcribed Image Text:X₁ 7. Let T: R³ R² be defined by TX₂ X3 = [x₁ + x₂] - 3x3 a) Prove that T is a Linear Transformation. b) Determine the Matrix of T, i.e., TX = AX. c) Determine dim(Ker T) and dim(Im T).
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