Part: a:Vertices of a parallelogram on a computer screen are given by the coordinates (3, 0), (6, 0), (4, 2) & (7, 2). If this parallelogram is being transformed in given order 1. x-scaling by factor 1/3 and y-scaling by factor 1/2 2. Translation of (1, -3) 3. Clockwise rotation of 30⁰ i. Write 3*3 matrices for each transformation. Representing the above parallelogram in form of data matrix, apply these transformations one by oneand drawthe parallelogram at each step ii. Find a single matrix for the composite transformation for above three transformations. Apply it to theparallelogram(data matrix)and draw it. Is it same with the one obtained in part į at last step.
Part: a:Vertices of a parallelogram on a computer screen are given by the coordinates (3, 0), (6, 0), (4, 2) & (7, 2). If this parallelogram is being transformed in given order 1. x-scaling by factor 1/3 and y-scaling by factor 1/2 2. Translation of (1, -3) 3. Clockwise rotation of 30⁰ i. Write 3*3 matrices for each transformation. Representing the above parallelogram in form of data matrix, apply these transformations one by oneand drawthe parallelogram at each step ii. Find a single matrix for the composite transformation for above three transformations. Apply it to theparallelogram(data matrix)and draw it. Is it same with the one obtained in part į at last step.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Linear Transformation and Applications:
Question # 3:
Part: a:Vertices of a parallelogram on a computer screen are given by the coordinates (3, 0),
(6, 0), (4, 2) & (7, 2). If this parallelogram is being transformed in given order
1. x-scaling by factor 1/3 and y-scaling by factor 1/2
2. Translation of (1, -3)
3. Clockwise rotation of 30°
i. Write 3*3 matrices for each transformation. Representing the above parallelogram in
form of data matrix, apply these transformations one by oneand drawthe
parallelogram at each step
ii. Find a single matrix for the composite transformation for above three transformations.
Apply it to theparallelogram(data matrix)and draw it. Is it same with the one
obtained in part į at last step.
Note: Deal all calculations with data matrix, not directly on the parallelogram.
Transcribed Image Text:Linear Transformation and Applications:
Question # 3:
Part: b:Let T from R? to R? be a linear transformation that maps en into yı and maps e, into
y2 where
e2=
yı
Find the image of any x = in R2under T.
Find the standard matrix of T?
Find the range of T?
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