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(f) Three of these transformations are shape-preserving. Which are they? UJ OK OL COM ON

(f) Three of these transformations are shape-preserving. Which are they? UJ OK OL COM ON

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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Each of J, K, L, M and N is a linear transformation from R2 to R2. These functions are given as follows: J(x1, x2) = (5x1 - 5x2, -10x1 + 10x2), K(x₁, x2)=(-√√5x2, √5x1), L(x₁, x₂) = (x2, -x₁), M(x1, x2) = (5x1 + 5x2, 10x1 - 6x2), N(x1, x2) = (-√√5x1, √5x2).
Transcribed Image Text:Each of J, K, L, M and N is a linear transformation from R2 to R2. These functions are given as follows: J(x1, x2) = (5x1 - 5x2, -10x1 + 10x2), K(x₁, x2)=(-√√5x2, √5x1), L(x₁, x₂) = (x2, -x₁), M(x1, x2) = (5x1 + 5x2, 10x1 - 6x2), N(x1, x2) = (-√√5x1, √5x2).
(f) Three of these transformations are shape-preserving. Which are they? UJ OK OL OM ON (g) One of these transformations is not injective. Which is it? (No answer given)
Transcribed Image Text:(f) Three of these transformations are shape-preserving. Which are they? UJ OK OL OM ON (g) One of these transformations is not injective. Which is it? (No answer given)
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