Let T: R³ R³ be the transformation that reflects each vector x = x₂ = 0 to the vector T(): = x1 -x2 X3 x1 2 through the plane X3 . Show that T is a linear transformation.
Let T: R³ R³ be the transformation that reflects each vector x = x₂ = 0 to the vector T(): = x1 -x2 X3 x1 2 through the plane X3 . Show that T is a linear transformation.
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:Let T : R³ → R³ be the transformation that reflects each vector
x₂ = 0 to the vector T(x)
=
x1
- x2
x 3
=
X1
x2
x3.
through the plane
. Show that T is a linear transformation.
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