3. Each of J, K, L, M and N is a linear transformation from R to R. These functions are given as follows: J(11, 12) = (5x1 – 3r2, –10z, + 6z2), K(I1,72) = (-22, I1), L(1, 72) = (2,1), M(z1,72) = (371 + 22, I1 + 2r2), N(1,12) = (-1, 72). (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? (d) One of these functions is an anti-clockwise rotation of the plane. Which is it? (e) One of these functions is a reflection over the vertical axis. Which is it?

3. Each of J, K, L, M and N is a linear transformation from R to R. These functions are given as follows: J(11, 12) = (5x1 – 3r2, –10z, + 6z2), K(I1,72) = (-22, I1), L(1, 72) = (2,1), M(z1,72) = (371 + 22, I1 + 2r2), N(1,12) = (-1, 72). (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? (d) One of these functions is an anti-clockwise rotation of the plane. Which is it? (e) One of these functions is a reflection over the vertical axis. Which is it?

Name: please explain part c thank you 3. Each of J, K, L, M and N is a linea
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Description: please explain part c thank you 3. Each of J, K, L, M and N is a linear transformation from R to R', These functionsare given as follows:J(11, 12) = (5x1 – 3z2, –10x1 + 672),K(x1, I2) = (-12, 1,),L(I1, 72) = (2, 1),M(I1,12) = (311 + I2, I1 + 2r2),N(r

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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