Answered: List the eigenvalues of A. The…

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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I am using an independent study program to learn linear algebra. In my course I came accross the attached slide.

I don't understand how, using the tangent formula given, the angle of rotation became -5pi/6.

Can you explain this?

List the eigenvalues of A. The transformation X→AX is the composition of a rotation and a scaling. Give the angle p of the
rotation, where - 1<@<n, and give the scale factor r.
- 7/3
7
A =
The eigenvalues are of the form 1 = a ± bi from the matrix
-7 -7/3
From the given matrix we have a = –7V3 and b = -7.
Thus, A = -7/3±7i
Next we use trigonometry to relate the angle o with sides - 7y3 and -7:
-7
tan
-7/3
1
= tan
V3
The scale factor is the magnitude of
the eigenvalues:
So p = -
5n
- since -n SY ST.
J(-7v3) + (-7)2 = 14
r =

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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