Lecture 9 Notes

Av v 0 a i v 0 deta i 0 1 1 det 0 4 1 matrix

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Unformatted text preview: is parallel to the position vector. • That is, Av = λv. Introduction to systems of equations • You should see two “special” directions. • What are they? • Directions along which the velocity vector is parallel to the position vector. Av = λv. √ λ2 = − 2 ￿ √￿ 1− 2 v2 = 1 • That is, Matrix review (eigen-calculations) • Find eigenvalues and eigenvectors of A= ￿ 1 4 ￿ 1 . 1 Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. Matrix review (eigen-calculations) ￿ ￿ 11 • Find eigenvalues and eigenvectors of A = . 41 • Looking for values λ and vectors v for which Av = λv. • What are the eigenvalues of A? (A) 1 and -3 (B) -1 and 3 (C) 1 and 3 (D) -1 and -3 (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. • What are the eigenvalues of A? (A) 1 and -3 (B) -1 and 3 (C) 1 and 3 (D) -1 and -3 (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. 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 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 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 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 Matrix review (eigen-calculations) ￿ ￿ 11...
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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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