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The matrices A1 A3 = [ ] A2 Го = [[ ]] A4 = Го 0] form a basis for the linear space V = M2×2. Write the matrix of the linear transformation T : M2×2 → M2×2 such that T(A) = 14A + 8AT relative to this basis. Let V be the plane with equation x1 - 3x2 - 2x3 = 0 in R³. The linear transformation T (F) X3. = 7 1 -107 -2 Xx2 X1 -2 2 -2 x 3. maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis +-188 A =

The matrices A1 A3 = [ ] A2 Го = [[ ]] A4 = Го 0] form a basis for the linear space V = M2×2. Write the matrix of the linear transformation T : M2×2 → M2×2 such that T(A) = 14A + 8AT relative to this basis. Let V be the plane with equation x1 - 3x2 - 2x3 = 0 in R³. The linear transformation T (F) X3. = 7 1 -107 -2 Xx2 X1 -2 2 -2 x 3. maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis +-188 A =

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
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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The matrices A1 A3 = [ ] A2 Го = [[ ]] A4 = Го 0] form a basis for the linear space V = M2×2. Write the matrix of the linear transformation T : M2×2 → M2×2 such that T(A) = 14A + 8AT relative to this basis.
Transcribed Image Text:The matrices A1 A3 = [ ] A2 Го = [[ ]] A4 = Го 0] form a basis for the linear space V = M2×2. Write the matrix of the linear transformation T : M2×2 → M2×2 such that T(A) = 14A + 8AT relative to this basis.
Let V be the plane with equation x1 - 3x2 - 2x3 = 0 in R³. The linear transformation T (F) X3. = 7 1 -107 -2 Xx2 X1 -2 2 -2 x 3. maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis +-188 A =
Transcribed Image Text:Let V be the plane with equation x1 - 3x2 - 2x3 = 0 in R³. The linear transformation T (F) X3. = 7 1 -107 -2 Xx2 X1 -2 2 -2 x 3. maps V into V so, by restricting it to V, we may regard it as a linear transformation T: V → V. Find the matrix A of the restricted map Ĩ: V → V with respect to the basis +-188 A =
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