9. Let the affine map A : R²→ R? be defined by A(x, y)(3x + 4, 2y – 3). Show thatthe image of a unit circle under A is an ellipse. Let||||= sup{|| A(x, y)|| | ||(x, y)|| < 1}be the norm of A. Indicate the vertex of the ellipse where A attains this norm.

Answered: Image /qna-images/answer/3154bea6-45c7-4336-98b4-4f31b8046c9a.jpg

Answered: 9. Let the affine map A : R? → R² be…

9. Let the affine map A : R? → R² be defined by A(x, y) = (3.x + 4, 2y – 3). Show that %3D the image of a unit circle under A is an ellipse. Let

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

9. Let the affine map A : R²
→ R? be defined by A(x, y)
(3x + 4, 2y – 3). Show that
the image of a unit circle under A is an ellipse. Let
||||
= sup{|| A(x, y)|| | ||(x, y)|| < 1}
be the norm of A. Indicate the vertex of the ellipse where A attains this norm.

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