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Let T be the triangle with vertices (x₁, y₁). (x2. y2), and (X3, 3), and let a с b d Let f be the matrix transformation defined by f(v) = Av for a vector v in R². First, compute the vertices of f(T) and the image of T under f, and then show that the area of f(T) is | det(A)] area of T.

Let T be the triangle with vertices (x₁, y₁). (x2. y2), and (X3, 3), and let a с b d Let f be the matrix transformation defined by f(v) = Av for a vector v in R². First, compute the vertices of f(T) and the image of T under f, and then show that the area of f(T) is | det(A)] area of T.

Advanced Engineering Mathematics
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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Let T be the triangle with vertices (x1, yı), (x2. ya), and (x3, ya), and let a b A = d Let f be the matrix transformation defined by f(v) = Av for a vector v in R. First, compute the vertices of f(T) and the image of T under f, and then show that the area of f(T) is | det(A)| area of T.
Transcribed Image Text:Let T be the triangle with vertices (x1, yı), (x2. ya), and (x3, ya), and let a b A = d Let f be the matrix transformation defined by f(v) = Av for a vector v in R. First, compute the vertices of f(T) and the image of T under f, and then show that the area of f(T) is | det(A)| area of T.
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