Let T be the linear transformation that is reflection across the line y = √√8x in R² followed by a stretch by a factor of 2. a. Find the eigenvalues and eigenvectors for T. b. Find the (standard) matrix for T. Hint for b. Use diagonalization.

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 77E
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Answer the question below:
Let T be the linear
transformation
that is
reflection across the line y = √√8x in R²
followed by a stretch by a factor of 2.
a. Find the eigenvalues and eigenvectors
for T.
b. Find the (standard) matrix for T.
Hint for b. Use diagonalization.
Transcribed Image Text:Let T be the linear transformation that is reflection across the line y = √√8x in R² followed by a stretch by a factor of 2. a. Find the eigenvalues and eigenvectors for T. b. Find the (standard) matrix for T. Hint for b. Use diagonalization.
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