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each eigenspace. A = 2 2 1 1 31 122 1 = 1 2 2 0 - 1 1 -2 0 500 010 001 1 1 - 00 8 -|+ 1 1 4 1 4 1 1 - 12 300 8 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are ₁ = eigenspaces are and , respectively. = C. In ascending order, the three distinct eigenvalues are ₁ corresponding eigenspaces are ++, and and A2 =. Bases for the corresponding 2₂ = , respectively. and 23 Bases for the

each eigenspace. A = 2 2 1 1 31 122 1 = 1 2 2 0 - 1 1 -2 0 500 010 001 1 1 - 00 8 -|+ 1 1 4 1 4 1 1 - 12 300 8 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are ₁ = eigenspaces are and , respectively. = C. In ascending order, the three distinct eigenvalues are ₁ corresponding eigenspaces are ++, and and A2 =. Bases for the corresponding 2₂ = , respectively. and 23 Bases for the

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 35EQ
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5.3 #2

Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. A = 22 1 1 3 1 122 = 1 2 2 1 0 - 1 1 - 2 0 500 0 1 0 001 1 1 - 100 |N|4 4 1 8 −1+ 4 →→ 2 4 1 1 - IN 1 3 9910 8 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ = eigenspaces are {and, respectively. A basis for the corresponding eigenspace is { and 22 =. Bases for the corresponding C. In ascending order, the three distinct eigenvalues are λ₁ = ₁^₂= corresponding eigenspaces are 4., and }, respectively. and 3 = Bases for the
Transcribed Image Text:Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. A = 22 1 1 3 1 122 = 1 2 2 1 0 - 1 1 - 2 0 500 0 1 0 001 1 1 - 100 |N|4 4 1 8 −1+ 4 →→ 2 4 1 1 - IN 1 3 9910 8 1 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ = eigenspaces are {and, respectively. A basis for the corresponding eigenspace is { and 22 =. Bases for the corresponding C. In ascending order, the three distinct eigenvalues are λ₁ = ₁^₂= corresponding eigenspaces are 4., and }, respectively. and 3 = Bases for the
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