We'll consider linear transformations in R3 and R3 that transform familiar geometric shapes.Find an invertible linear transformation that maps the uni circle x2+y2=1 to the ellipse 1/4x2+1/9y2=1. By "maps the circle to the ellipse," we mean that every vector lying on the circle is sent to a vector lying on the ellipse. Is your answer unique? Justify rigorously.

We'll consider linear transformations in R3 and R3 that transform familiar geometric shapes.Find an invertible linear transformation that maps the uni circle x2+y2=1 to the ellipse 1/4x2+1/9y2=1. By "maps the circle to the ellipse," we mean that every vector lying on the circle is sent to a vector lying on the ellipse. Is your answer unique? Justify rigorously.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 45E

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Question

We'll consider linear transformations in R3 and R3 that transform familiar geometric shapes.

Find an invertible linear transformation that maps the uni circle x²+y²=1 to the ellipse 1/4x²+1/9y²=1. By "maps the circle to the ellipse," we mean that every vector lying on the circle is sent to a vector lying on the ellipse. Is your answer unique? Justify rigorously.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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