Lecture 9 Notes

# 41 looking for values and vectors v for which av v av

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Unformatted text preview: • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 (λ − 2λ − 3 = 0) 2 Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 (λ − 2λ − 3 = 0) λ = 1 ± 2 = −1, 3 2 Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 (λ − 2λ − 3 = 0) λ = 1 ± 2 = −1, 3 • What are the eigenvectors associated with λ￿ ￿ 1=-1? (A) v1 (B) v1 (C) v1 2 (D) v1 1 = −2 ￿￿ 1 =c −2 ￿￿ 2 = 1 ￿￿ 2 =c 1 (E) Explain, please. Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 (λ − 2λ − 3 = 0) λ = 1 ± 2 = −1, 3 • What are the eigenvectors associated with λ￿ ￿ 1=-1? (A) v1 (B) v1 (C) v1 2 (D) v1 1 = −2 ￿￿ 1 =c −2 ￿￿ 2 = 1 ￿￿ 2 =c 1 (E) Explain, please. Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Av − λ v = 0 (A − λI )v = 0 det(A − λI ) = 0 ￿ ￿ 1−λ 1 det =0 4 1−λ (1 − λ) − 4 = 0 2 (λ − 2λ − 3 = 0) λ = 1 ± 2 = −1, 3 2 Matrix review (ei...
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## This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.

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