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Write down the matrix of the linear transformation f that maps (1, 0) to (3, 1) and (0, 1) to (-1,1). Show that f is invertible and find the matrix of f-¹. Find the equation of the image of the unit circle x² + y² = 1 under the linear transformation f. Write your answer in the form ax² + bxy + cy² = d, where a, b, c and d are integers whose values you should find.

Write down the matrix of the linear transformation f that maps (1, 0) to (3, 1) and (0, 1) to (-1,1). Show that f is invertible and find the matrix of f-¹. Find the equation of the image of the unit circle x² + y² = 1 under the linear transformation f. Write your answer in the form ax² + bxy + cy² = d, where a, b, c and d are integers whose values you should find.

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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(a) (i) (ii) (iii) Write down the matrix of the linear transformation f that maps (1, 0) to (3, 1) and (0, 1) to (-1,1). Show that f is invertible and find the matrix of f-¹. Find the equation of the image of the unit circle x² + y² = 1 under the linear transformation f. Write your answer in the form ax² + bxy + cy2 = d, where a, b, c and d are integers whose values you should find.
Transcribed Image Text:(a) (i) (ii) (iii) Write down the matrix of the linear transformation f that maps (1, 0) to (3, 1) and (0, 1) to (-1,1). Show that f is invertible and find the matrix of f-¹. Find the equation of the image of the unit circle x² + y² = 1 under the linear transformation f. Write your answer in the form ax² + bxy + cy2 = d, where a, b, c and d are integers whose values you should find.
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