4. Say W = {(x, y, z) ER³: x-y-2z = 0} < R³. a) Find [RW], where Rwy is the reflection about W, and E is the standard basis of R³. b) Compute Rw(v) when v = (3,0,1). c) Find the eigenvalues and eigenvectors of [RW]E- (Note: you may compute these directly, or appeal to some geometrically 'convenient' vectors.)
4. Say W = {(x, y, z) ER³: x-y-2z = 0} < R³. a) Find [RW], where Rwy is the reflection about W, and E is the standard basis of R³. b) Compute Rw(v) when v = (3,0,1). c) Find the eigenvalues and eigenvectors of [RW]E- (Note: you may compute these directly, or appeal to some geometrically 'convenient' vectors.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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![4. Say W = {(x, y, z) ER³: x-y-2z = 0} < R³.
a) Find [RW], where Rwy is the reflection about W, and E is the standard basis of R³.
b) Compute Rw(v) when v = (3,0,1).
c) Find the eigenvalues and eigenvectors of [RW]E-
(Note: you may compute these directly, or appeal to some geometrically 'convenient'
vectors.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ee7c6b4-fb4c-4f4d-81f2-c90722bbf703%2F968fe17e-2848-4a07-9410-b74090f8c8b4%2Foitqwgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Say W = {(x, y, z) ER³: x-y-2z = 0} < R³.
a) Find [RW], where Rwy is the reflection about W, and E is the standard basis of R³.
b) Compute Rw(v) when v = (3,0,1).
c) Find the eigenvalues and eigenvectors of [RW]E-
(Note: you may compute these directly, or appeal to some geometrically 'convenient'
vectors.)
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