For each of the following matrices A, find an invertible matrix QE M₂ (R), a positive real numbers, and a rotation matrix R such that QAQ SR. You do not need to find the angle of rotation of the rotation matrix R. = (a) A = 9 4 -13 -3

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.4: Determinants
Problem 53PS
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H3.

 

For each of the following matrices A, find an invertible matrix Q € M₂ (R), a positive real numbers, and a rotation matrix R such that
Q¹AQ = SR. You do not need to find the angle of rotation of the rotation matrix R.
(a)
(b)
A =
4
-13 -3
|-
9
5
4-[33]
A =
-6
Transcribed Image Text:For each of the following matrices A, find an invertible matrix Q € M₂ (R), a positive real numbers, and a rotation matrix R such that Q¹AQ = SR. You do not need to find the angle of rotation of the rotation matrix R. (a) (b) A = 4 -13 -3 |- 9 5 4-[33] A = -6
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