Let T be the linear transformation which takes a vector in R² and does the following in sequence: • Shears it by a factor of 3 in the x-direction, • Reflects it over the y-axis, • Rotates it 90° clockwise about the origin, and finally • Dilates it by a factor of 9. a) Find the matrix associated with T. b) Prove that the transformation is linear through explicit calculation.
Let T be the linear transformation which takes a vector in R² and does the following in sequence: • Shears it by a factor of 3 in the x-direction, • Reflects it over the y-axis, • Rotates it 90° clockwise about the origin, and finally • Dilates it by a factor of 9. a) Find the matrix associated with T. b) Prove that the transformation is linear through explicit calculation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let T be the linear transformation which takes a vector in R² and does the
following in sequence:
• Shears it by a factor of 3 in the x-direction,
• Reflects it over the y-axis,
• Rotates it 90° clockwise about the origin, and finally
• Dilates it by a factor of 9.
a) Find the matrix associated with T.
b) Prove that the transformation is linear through explicit calculation.
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