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Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section: Chapter Questions

Problem 6CLR

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Question

Consider the linear transformation T: Rⁿ→Rⁿ whose matrix A relative to the standard basis is given. Find (a) the eigenvalues of A, (b) a basis for each of the corresponding eigenspaces, and (c) the matrix A′ for T relative to the basis B′, where B′ is made up of the basis vectors found in part (b).

Expert Solution

Step 1: Given information:

Given matrix of a linear transformation

Step 2: Calculation of eigen values

The characteristics equation of A,

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