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Consider a linear transformation T: R² R2 and a basis B = (₁, ₂) of R² with and T(₂)=40+30₂. T(₁)=36₁ +₂ T= | Tenis Ti (a) Find the B-matrix of T. (b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the matrix that induces T. (c) Find the eigenvalues of the matrix that induces T. mix that induces T as a linear combination

Consider a linear transformation T: R² R2 and a basis B = (₁, ₂) of R² with and T(₂)=40+30₂. T(₁)=36₁ +₂ T= | Tenis Ti (a) Find the B-matrix of T. (b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the matrix that induces T. (c) Find the eigenvalues of the matrix that induces T. mix that induces T as a linear combination

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(5) Consider a linear transformation T: R² R² and a basis B = (₁, ₂) of R² with T(₁) = 30₁ + ₂ and T(₂)=401+302. T= | Tov) TUB) = (a) Find the B-matrix of T. (b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the matrix that induces T. (c) Find the eigenvalues of the matrix that induces T. (d) Let S = [₁ 2], find the eigenvectors of the matrix that induces T as a linear combination of ₁ and ₂.
Transcribed Image Text:(5) Consider a linear transformation T: R² R² and a basis B = (₁, ₂) of R² with T(₁) = 30₁ + ₂ and T(₂)=401+302. T= | Tov) TUB) = (a) Find the B-matrix of T. (b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the matrix that induces T. (c) Find the eigenvalues of the matrix that induces T. (d) Let S = [₁ 2], find the eigenvectors of the matrix that induces T as a linear combination of ₁ and ₂.
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