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Exercise 4.13 Consider the subspace 2 1 - ( ) ( ) ( ! ) 200 0 2 0 002 1 002 2 1 CM (3 × 3, R). 002 a) Determine the subset S of matrices of W admitting 2 as eigenvalue. Is S a subspace? Is it a linear variety? b) Determine which among the matrices of S are diagonalisable. c) Determine which among the matrices of S are similar to a Jordan matrix with a single block.

Exercise 4.13 Consider the subspace 2 1 - ( ) ( ) ( ! ) 200 0 2 0 002 1 002 2 1 CM (3 × 3, R). 002 a) Determine the subset S of matrices of W admitting 2 as eigenvalue. Is S a subspace? Is it a linear variety? b) Determine which among the matrices of S are diagonalisable. c) Determine which among the matrices of S are similar to a Jordan matrix with a single block.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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Exercise 4.13 Consider the subspace 200 W = ( 0 2 0 002 1 210 020 002 1 2 021 002 CM(3 x 3, R). a) Determine the subset S of matrices of W admitting 2 as eigenvalue. Is S a subspace? Is it a linear variety? b) Determine which among the matrices of S are diagonalisable. c) Determine which among the matrices of S are similar to a Jordan matrix with a single block.
Transcribed Image Text:Exercise 4.13 Consider the subspace 200 W = ( 0 2 0 002 1 210 020 002 1 2 021 002 CM(3 x 3, R). a) Determine the subset S of matrices of W admitting 2 as eigenvalue. Is S a subspace? Is it a linear variety? b) Determine which among the matrices of S are diagonalisable. c) Determine which among the matrices of S are similar to a Jordan matrix with a single block.
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