(a) identify the transformation, and (b) graphically represent the transform

ushwaui 2021-11-18 Answered
(a) identify the transformation, and
(b) graphically represent the transformation for an arbitrary vector in R2.
T(x, y) = (x, 2y)
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Expert Answer

Lupe Kirkland
Answered 2021-11-19 Author has 21 answers
Step 1
Given:
The linear transformation is T(x.) =(x.2y)
(a)
It is observed that the transformation doubles the vy —coordinate. Thus, it is a vertical expansion.
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George Burge
Answered 2021-11-20 Author has 16 answers

Step 2
(b)
The following graph shows the given transformation,
image

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Approximating y ( t n ) at the relation y ( t n ) = f ( t n , y ( t n ) ) with the difference quotient [ y ( t n + 1 ) y ( t n ) h ] we get to the Euler method.
Approximating the same derivative with the quotient [ y ( t n ) y ( t n 1 ) h ] we get to the backward Euler method
y n + 1 = y n + h f ( t n + 1 , y n + 1 ) , n = 0 , , N 1
where y 0 := y 0 .
In order to find the formula for the forward Euler method, we use the limit lim h 0 y ( x 0 + h ) y ( x 0 ) h for x 0 = t n , h = t n + 1 t n .
In order to find the formula for the backward Euler method, could we pick h = t n 1 t n although it is negative?
Or how do we get otherwise to the approximation:
y ( t n ) y ( t n ) y ( t n 1 ) h

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