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 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
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 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
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.5: Applications Of Linear Transformations
Problem 53E
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Matrices And Algebra.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02736ba4-9bb4-4949-999c-6b1cc8a9bc96%2Fd30de626-c1f7-49fe-b9dc-067c80ecdfb4%2Fnhmssad_processed.jpeg&w=3840&q=75)
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.
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02736ba4-9bb4-4949-999c-6b1cc8a9bc96%2Fd30de626-c1f7-49fe-b9dc-067c80ecdfb4%2Fwvg0rch_processed.jpeg&w=3840&q=75)
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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