Let T: IR2 > R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a=() is orthogonal to the line in question and the vector b = (;) is on this line, a) Give T (a) and T (b) (think about the geometry of reflection) b) Give the canonical matrix of T. Hint: use a) and an inverse matrix c) Express the vector e - 6) as a linear combination of a and b and using linearity of T, give T (e1). Do the same with - () d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the vector (3) in relation to the line in question.
Let T: IR2 > R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back that the vector a=() is orthogonal to the line in question and the vector b = (;) is on this line, a) Give T (a) and T (b) (think about the geometry of reflection) b) Give the canonical matrix of T. Hint: use a) and an inverse matrix c) Express the vector e - 6) as a linear combination of a and b and using linearity of T, give T (e1). Do the same with - () d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the vector (3) in relation to the line in question.
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:5)
Let T: R2 → R2 reflection (or orthogonal symmetry) with respect to the line 2x - y = 0. We call back
that the vector a= (-). is orthogonal to the line in question and the vector b = () is on this
line,
a) Give T (a) and T (b) (think about the geometry of reflection)
b) Give the canonical matrix of T. Hint: use a) and an inverse matrix
c) Express the vector e1 =
6) as a linear combination of a and b and using linearity
of T, give T (e1). Do the same with ez
d) Using c), find the canonical matrix of T and give the vector obtained by the reflection of the
(3) in relation to the line in question.
vector
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