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Suppose that A is a 6 X 6 matrix with characteristic polynomial cA(λ) = (1 + λ)(1 -λ)2(2 - λ)3• Prove that it is not possible to find three linearly in independent vectors v1, v2, v3 in R6 such that Av1 = v1, Av2 = v2, and Av3 = v3. (b) If A is diagonalizable, what are the dimensions of the eigenspaces E _1, E1, and E2?

Suppose that A is a 6 X 6 matrix with characteristic polynomial cA(λ) = (1 + λ)(1 -λ)2(2 - λ)3• Prove that it is not possible to find three linearly in independent vectors v1, v2, v3 in R6 such that Av1 = v1, Av2 = v2, and Av3 = v3. (b) If A is diagonalizable, what are the dimensions of the eigenspaces E _1, E1, and E2?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Suppose that A is a 6 X 6 matrix with characteristic polynomial cA(λ) = (1 + λ)(1 -λ)2(2 - λ)3• Prove that it is not possible to find three linearly in independent vectors v1, v2, v3 in R6 such that Av1 = v1, Av2 = v2, and Av3 = v3. (b) If A is diagonalizable, what are the dimensions of the eigenspaces E _1, E1, and E2?

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