2. Let T : R2 → R² be a linear transformation, and suppose [T], the standard matrix representation of T, is given by [T] || (a) Calculate T(1,1) and T(-1, 1). Use your answer to sketch how the square corresponding to the vectors (1,1) and (–1, 1) is transformed when applying T. (b) What property of [T] implies the transformed square in (a) has the same area as the original square, and also involves a reflection? Clearly state the theory being used. (c) Give a geometrical specification of T.
2. Let T : R2 → R² be a linear transformation, and suppose [T], the standard matrix representation of T, is given by [T] || (a) Calculate T(1,1) and T(-1, 1). Use your answer to sketch how the square corresponding to the vectors (1,1) and (–1, 1) is transformed when applying T. (b) What property of [T] implies the transformed square in (a) has the same area as the original square, and also involves a reflection? Clearly state the theory being used. (c) Give a geometrical specification of T.
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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Could someone help with parts a,b,c
![2. Let T : R? → R² be a linear transformation, and suppose [T], the standard matrix representation
of T, is given by
[T]
(a) Calculate T(1,1) and T(-1, 1). Use your answer to sketch how the square corresponding
to the vectors (1,1) and (-1, 1) is transformed when applying T.
(b) What property of [T] implies the transformed square in (a) has the same area as the original
square, and also involves a reflection? Clearly state the theory being used.
(c) Give a geometrical specification of T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb259e400-52cb-4f05-8918-861040ba5689%2Fcdb4810f-ad3e-4180-9731-68c57851bfbe%2F7hzic5_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let T : R? → R² be a linear transformation, and suppose [T], the standard matrix representation
of T, is given by
[T]
(a) Calculate T(1,1) and T(-1, 1). Use your answer to sketch how the square corresponding
to the vectors (1,1) and (-1, 1) is transformed when applying T.
(b) What property of [T] implies the transformed square in (a) has the same area as the original
square, and also involves a reflection? Clearly state the theory being used.
(c) Give a geometrical specification of T.
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