3. Each of J, K, L, M and N is a linear transformation from R2 to R?. These functions are given as follows: J(11, 12) = (5x1-372,-10z1+6x2), K(1, T2) = (-I2, 1), L(I1, 12) = (12, I1), M(1, 12) = (31+2, I1 + 212), N(11, T2) = (-I1, 12). %3D %3D (a) In each case, write down the matrix of the transformation and compute its deter- minant. (b) Sketch a picture indicating what happens to the standard basis {(1,0), (0, 1)} un- der each function. (c) One of these functions is not injective. Which is it?

3. Each of J, K, L, M and N is a linear transformation from R2 to R?. These functions are given as follows: J(11, 12) = (5x1-372,-10z1+6x2), K(1, T2) = (-I2, 1), L(I1, 12) = (12, I1), M(1, 12) = (31+2, I1 + 212), N(11, T2) = (-I1, 12). %3D %3D (a) In each case, write down the matrix of the transformation and compute its deter- minant. (b) Sketch a picture indicating what happens to the standard basis {(1,0), (0, 1)} un- der each function. (c) One of these functions is not injective. Which is it?

Name: Part (c) Please explain what makes something injective or not 3. Each
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Description: Part (c) Please explain what makes something injective or not 3. Each of J, K, L, M and N is a linear transformation from R2 to R?. These functionsare given as follows:J(11, 12) = (5x1-372,-10z1+6x2),K(1, T2) = (-I2, 1),L(I1, 12) = (12, I1),M(1, 12)

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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