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?
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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Q3
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(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 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?
(No answer given) ♦
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