Cross product is a linear transformation from R³ →R³ You can define it as X1 X2 X3 X Y1 Y2 Y3 = det( = e₁ X1 e2 → ez Y1 Y2 X3 Y3 Define the linear transformation Tas x2 Note that this is the determinant of a matrix that has vectors as some of the entries. You can look at section 3.6 in the textbook for alternate definitions. T(x) = x x 2 3 a. Compute T(ei), T(ez), Te) b. Use your answer from a. to write the standard matrix of the linear transformation T c. Use your answer from b. to compute T( 4 3
Cross product is a linear transformation from R³ →R³ You can define it as X1 X2 X3 X Y1 Y2 Y3 = det( = e₁ X1 e2 → ez Y1 Y2 X3 Y3 Define the linear transformation Tas x2 Note that this is the determinant of a matrix that has vectors as some of the entries. You can look at section 3.6 in the textbook for alternate definitions. T(x) = x x 2 3 a. Compute T(ei), T(ez), Te) b. Use your answer from a. to write the standard matrix of the linear transformation T c. Use your answer from b. to compute T( 4 3
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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Transcribed Image Text:Cross product is a linear transformation from
R³ →R³
You can define it as
X1
X2
X3
X
Yı
Y2
Y3
e₁ X1 Y1
x2
Y2
Y3
=
= det( e2
→
ez
X3
Note that this is the determinant of a matrix that has
vectors as some of the entries. You can look at
section 3.6 in the textbook for alternate definitions.
Define the linear transformation Tas
T(x) = x x 2
3
a. Compute T(ei), T(₂), Te)
b. Use your answer from a. to write the standard
matrix of the linear transformation T
c. Use your answer from b. to compute T(
4
H
3
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