Explanation Given: The mapping G ( u , v ) = ( 2 u + v , 5 u + 3 v ) Calculation: Since ( x , y ) = G ( u , v ) = ( 2 u + v , 5 u + 3 v ) . Therefore, x = 2 u + v , y = 5 u + 3 v v = x − 2 u Substitute v = x − 2 u in y = 5 u + 3 v we get y = 5 u + 3 ( x − 2 u ) y = 5 u + 3 x − 6 u y = 3 x − u u = 3 x − y Therefore, v = x − 2 ( 3 x − y ) v = x − 6 x + 2 y v = − 5

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.6, Problem 8E

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To describe:

$G (u, v) = (2 u + v, 5 u + 3 v)$ maps the line $v = m u$ to the line of slope $\frac{5 + 3 m}{2 + m}$ through the origin in the $x y$ plane.

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Chapter 16.6, Problem 7E

Chapter 16.6, Problem 9E

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G ( u , v ) = ( 2 u + v , 5 u + 3 v ) maps the line v = m u to the line of slope 5 + 3 m 2 + m through the origin in the x y plane.

Solution Summary: The author explains the mapping of the line v = m u to the slope 5 + 3

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To describe:

$G (u, v) = (2 u + v, 5 u + 3 v)$ maps the line $v = m u$ to the line of slope $\frac{5 + 3 m}{2 + m}$ through the origin in the $x y$ plane.

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Chapter 16 Solutions

G ( u , v ) = ( 2 u + v , 5 u + 3 v ) maps the line v = m u to the line of slope 5 + 3 m 2 + m through the origin in the x y plane.

Solution Summary: The author explains the mapping of the line v = m u to the slope 5 + 3

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To describe: G(u,v)=(2u+v,5u+3v)maps the line v=muto the line of slope 5+3m2+m through the origin in the xyplane.

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Chapter 16 Solutions

To describe:

$G (u, v) = (2 u + v, 5 u + 3 v)$ maps the line $v = m u$ to the line of slope $\frac{5 + 3 m}{2 + m}$ through the origin in the $x y$ plane.