7. For R, let A = Ag = cos sin sin 0 cos sin 0 and B Be= 86). cos cos sin (a) Show that B has an eigenvector v = (cos(0/2), sin(0/2)) with eigenvalue 1, and a second, orthogonal, eigenvector with eigen- value -1. Conclude that this matrix represents a reflection in the line tha li 9/9

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
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7. For R, let
A = Ag =
cos sin 0
sin
(540) and B = Be=
cos
cos
sin 0
(a) Show that B has an eigenvector v = (cos(0/2), sin(0/2)) with
eigenvalue 1, and a second, orthogonal, eigenvector with eigen-
value -1. Conclude that this matrix represents a reflection in the
line through 0 with inclination 0/2.
Transcribed Image Text:7. For R, let A = Ag = cos sin 0 sin (540) and B = Be= cos cos sin 0 (a) Show that B has an eigenvector v = (cos(0/2), sin(0/2)) with eigenvalue 1, and a second, orthogonal, eigenvector with eigen- value -1. Conclude that this matrix represents a reflection in the line through 0 with inclination 0/2.
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