Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and, interpreting T as a matrix, det(T) ‡ 0. Let P be the parallelogram which is the image of the square D = [0, 1] × [0, 1] (i.e. T(D) =P). Then the area of P is given by Olad - bel ad - bc abcd 1 lad - bc| Olabcd\
Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and, interpreting T as a matrix, det(T) ‡ 0. Let P be the parallelogram which is the image of the square D = [0, 1] × [0, 1] (i.e. T(D) =P). Then the area of P is given by Olad - bel ad - bc abcd 1 lad - bc| Olabcd\
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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![Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and,
interpreting T as a matrix, det(T) # 0. Let P be the parallelogram which is the image of the square D = = [0, 1] × [0, 1] (i.e.
T(D) =P). Then the area of P is given by
O lad - bcl
ad bc
abcd
1
|ad - bc|
O labcd|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccceb61d-0b39-4729-973d-5eeee6d6d189%2Fed02f936-6b06-4311-9b3b-773c55dd31dc%2Fdnzr02_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are real numbers and,
interpreting T as a matrix, det(T) # 0. Let P be the parallelogram which is the image of the square D = = [0, 1] × [0, 1] (i.e.
T(D) =P). Then the area of P is given by
O lad - bcl
ad bc
abcd
1
|ad - bc|
O labcd|
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