8) Under the bilinear transformation w=u+iv=iz, the image of the infinite strip 0

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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8) Under the bilinear transformation w = u + iv=iz, the image of the
in finite strip 0<x< 1, is given by
0<v<1
0<u<1
9) Under the bilinear transformation that maps - 1, 0 and 1 to -i, 1 and i, respectively, the interior of the unit circle
in the w-plane is mapped into
O
the interior of the unit circle in the 2 - plane
O
the exterior of the unit circle in the z - plane
O
the upper half of the 2 - plane
O
the lower half of the z-plane
10) The image of the strip - <y< , under the transformation
tanh(),
B
O O OO
1/1/213
<1
w <2
|w| < 1/1/20
), is
Transcribed Image Text:8) Under the bilinear transformation w = u + iv=iz, the image of the in finite strip 0<x< 1, is given by 0<v<1 0<u<1 9) Under the bilinear transformation that maps - 1, 0 and 1 to -i, 1 and i, respectively, the interior of the unit circle in the w-plane is mapped into O the interior of the unit circle in the 2 - plane O the exterior of the unit circle in the z - plane O the upper half of the 2 - plane O the lower half of the z-plane 10) The image of the strip - <y< , under the transformation tanh(), B O O OO 1/1/213 <1 w <2 |w| < 1/1/20 ), is
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