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4. Let T be a rotation by 90° (clockwise), as a linear transformation from R2 to R2. Let S be a reflection in the x-axis, as a linear transformation from R2 to R². (a) Find the matrix A of T. (b) Find the matrix B of S (c) Find the matrix of a 90° rotation followed by a reflection in the x-axis. Consider the images of B e₁ = and e₂ = A under this transformation, and describe what it does geometrically.

4. Let T be a rotation by 90° (clockwise), as a linear transformation from R2 to R2. Let S be a reflection in the x-axis, as a linear transformation from R2 to R². (a) Find the matrix A of T. (b) Find the matrix B of S (c) Find the matrix of a 90° rotation followed by a reflection in the x-axis. Consider the images of B e₁ = and e₂ = A under this transformation, and describe what it does geometrically.

Advanced Engineering Mathematics
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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4. Let T be a rotation by 90° (clockwise), as a linear transformation from R2 to R2. Let S be a reflection in the x-axis, as a linear transformation from R2 to R². (a) Find the matrix A of T. (b) Find the matrix B of S (c) Find the matrix of a 90° rotation followed by a reflection in the x-axis. Consider the images of B e₁ = and e₂ = 8 under this transformation, and describe what it does geometrically. (d) Find the matrix of a reflection in the x-axis followed by a rotation of 90°. Consider the images of e₁ and e2 under this transformation, and describe what it does geometrically.
Transcribed Image Text:4. Let T be a rotation by 90° (clockwise), as a linear transformation from R2 to R2. Let S be a reflection in the x-axis, as a linear transformation from R2 to R². (a) Find the matrix A of T. (b) Find the matrix B of S (c) Find the matrix of a 90° rotation followed by a reflection in the x-axis. Consider the images of B e₁ = and e₂ = 8 under this transformation, and describe what it does geometrically. (d) Find the matrix of a reflection in the x-axis followed by a rotation of 90°. Consider the images of e₁ and e2 under this transformation, and describe what it does geometrically.
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