part e. 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,, 12) = (-1,12).(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?

Linear Transformation from R2 to R2 is given, we have to find transformation is a reflection over…

3. Each of J, K, L, M and N is a linear transformation from R' to R. These functions are given as follows: J(r1, 12) = (5z - 3r2,-10r, + 6z), K(x1, 72) = (-12, 1), L(x1, 72) = (2, 1), M(1, 12) = (3r, + 22, I1 + 2x3), N(*1, 12) - (-1, 1).

3. Each of J, K, L, M and N is a linear transformation from R' to R. These functions are given as follows: J(r1, 12) = (5z - 3r2,-10r, + 6z), K(x1, 72) = (-12, 1), L(x1, 72) = (2, 1), M(1, 12) = (3r, + 22, I1 + 2x3), N(*1, 12) - (-1, 1).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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part e.

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 – 3z2, –10x1 + 672),
K(x1, I2) = (-12, 1,),
L(I1, 72) = (2, 1),
M(I1,12) = (311 + I2, I1 + 2r2),
N(r,, 12) = (-1,12).
(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?

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