Let v1 = (1,−1,1),v2 = (2,1,3), and v3 = (−1,−1,2) be eigenvectors of the matrix A corresponding to the eigenvalues λ1 = 2,λ2 =− 2, and λ3 =3, respectively, and let v=(5,0,3). Q. Express v as a linear combination of v1,v2, and v3.

Let v1 = (1,−1,1),v2 = (2,1,3), and v3 = (−1,−1,2) be eigenvectors of the matrix A corresponding to the eigenvalues λ1 = 2,λ2 =− 2, and λ3 =3, respectively, and let v=(5,0,3). Q. Express v as a linear combination of v1,v2, and v3.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 75E

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Question

Let v₁ = (1,−1,1),v₂ = (2,1,3), and v₃ = (−1,−1,2) be eigenvectors of the matrix A corresponding to the eigenvalues λ₁ = 2,λ₂ =− 2, and λ₃ =3, respectively, and let v=(5,0,3).

Q. Express v as a linear combination of v₁,v₂, and v₃.

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