Explanation Given: Let R 0 = [ 0 , 1 ] × [ 0 , 1 ] be the unit square. The translate of a map G 0 ( u , v ) = ( ϕ ( u , v ) , ψ ( u , v ) ) is a map G ( u , v ) = ( a + ϕ ( u , v ) , b + ψ ( u , v ) ) where a,b are constants. The map G 0 in the given figure maps R 0 to the parallelogram P 0 and that the translate G 1 = ( 2 + 4 u + 2 v , 1 + u + 3 v ) maps R 0 to P 1 . The parallelogram is given which is spanned by the vectors 〈 3 , 9 〉 , 〈 − 4 , 6 〉 base at ( 4 , 2 ) . Calculation: Consider the parallelogram P spanned by the vectors 〈 3 , 9 〉 , 〈 − 4 , 6 〉 base at ( 4 , 2 ) . It means that the parallelogram has the following three vertices: A = ( 4 , 2 ) B = ( 7 , 11 ) D = ( 0 , 8 ) The sketch of the parallelogram is as shown below:

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.6, Problem 28E

To determine

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The translate of a linear mapping that maps $R_{0}$ to the parallelogram spanned by given vectors.

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Chapter 16.6, Problem 27E

Chapter 16.6, Problem 29E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The translate of a linear mapping that maps R 0 to the parallelogram spanned by given vectors .

Solution Summary: The author calculates the translate of a linear mapping that maps R 0 to the parallelogram spanned by given vectors.

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The translate of a linear mapping that maps $R_{0}$ to the parallelogram spanned by given vectors.

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Chapter 16 Solutions

The translate of a linear mapping that maps R 0 to the parallelogram spanned by given vectors .

Solution Summary: The author calculates the translate of a linear mapping that maps R 0 to the parallelogram spanned by given vectors.

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To calculate: The translate of a linear mapping that maps R0to the parallelogram spanned by given vectors.

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Chapter 16 Solutions

To calculate:

The translate of a linear mapping that maps $R_{0}$ to the parallelogram spanned by given vectors.