Q3 Each of J, K, L, M and N is a linear transformation from R2 to R2. These functions are given as follows:J(21, 22) = (5x15x2, -10x1 +102),K(T1, 12) =(√5x2, √5x1),L(1,2)=(2, -1),M(x1, x2) = (5x1 + 5x2, 10x1 - 6x2),N(1, 2) = (-√5x1, √5x2).(a) In each case, compute the determinant of the transformationdet J=,det K=det L-,det M=det N=(b) One of these transformations involves a reflection in the vertical axis and a rescaling. Which is it?(No answer given) ♦

a) J(x1,x2)=(5x1-5x2,-10x1+10x2)=5-5-1010x1x2det J=5-5-1010=50-50=0K(x1,x2)=(-5x2,5x1)…

Each of J, K, L, M and N is a linear transformation from R2 to R2. These functions are given as follows: J(21, 22) = (5x15x2,-101 +102), K(1,2)=(√5x2, √5x1), L(1,2)=(2, -1), M(x1, x2) = (5x1 + 5x2, 10x1 - 6x2), N(1, ₂) = (-√51, √5x2). (a) In each case, compute the determinant of the transformation det J- det K- det L- ,det M- det N- (b) One of these transformations involves a reflection in the vertical axis and a rescaling. Which is it?

Each of J, K, L, M and N is a linear transformation from R2 to R2. These functions are given as follows: J(21, 22) = (5x15x2,-101 +102), K(1,2)=(√5x2, √5x1), L(1,2)=(2, -1), M(x1, x2) = (5x1 + 5x2, 10x1 - 6x2), N(1, ₂) = (-√51, √5x2). (a) In each case, compute the determinant of the transformation det J- det K- det L- ,det M- det N- (b) One of these transformations involves a reflection in the vertical axis and a rescaling. Which is it?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 3EQ

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