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Matrix Representation of a Linear Mapping Consider the operator TE L(R²) (recall that an operator is a linear mapping T : V → W, where V = W) defined by 5x - 3y -3x + 5y T(x, y) = for any x, y € R. Find the matrix M(T, (₁, ₂), (₁, ₂)) representing the mapping (definition 3.32) in the following basis of V=W = R²: (a) the canonical basis v₁ = (1,0), ₂ = (0, 1)); (b) v₁ = (1,0), v2 = (1, 1); (c) v₁ = (1, 1), ₂= (1, -1). For each of the matrices you find calculate its trace and determinant.

Matrix Representation of a Linear Mapping Consider the operator TE L(R²) (recall that an operator is a linear mapping T : V → W, where V = W) defined by 5x - 3y -3x + 5y T(x, y) = for any x, y € R. Find the matrix M(T, (₁, ₂), (₁, ₂)) representing the mapping (definition 3.32) in the following basis of V=W = R²: (a) the canonical basis v₁ = (1,0), ₂ = (0, 1)); (b) v₁ = (1,0), v2 = (1, 1); (c) v₁ = (1, 1), ₂= (1, -1). For each of the matrices you find calculate its trace and determinant.

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
Section6.4: Transistion Matrices And Similarity
Problem 39E
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Matrix Representation of a Linear Mapping Consider the operator TE L(R²) (recall that an operator is a linear mapping T: V → W, where V=W) defined by T(x, y) = 5x - 3y -3x + 5y 4 for any z, y € R. Find the matrix M(T, (v₁, ₂), (V₁, V₂)) representing the mapping (definition 3.32) in the following basis of V=W = R²: (a) the canonical basis v₁ = (1,0), v2 = (0,1)); (b) v₁ = (1,0), v2 = (1, 1); (c) v₁ = (1, 1), v₂ = (1, -1). For each of the matrices you find calculate its trace and determinant.
Transcribed Image Text:Matrix Representation of a Linear Mapping Consider the operator TE L(R²) (recall that an operator is a linear mapping T: V → W, where V=W) defined by T(x, y) = 5x - 3y -3x + 5y 4 for any z, y € R. Find the matrix M(T, (v₁, ₂), (V₁, V₂)) representing the mapping (definition 3.32) in the following basis of V=W = R²: (a) the canonical basis v₁ = (1,0), v2 = (0,1)); (b) v₁ = (1,0), v2 = (1, 1); (c) v₁ = (1, 1), v₂ = (1, -1). For each of the matrices you find calculate its trace and determinant.
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