[2 1 4. Let A = 1 1 -1 2 -1 2 Show that the characteristic polynomial fa of A is -X³ + 5A² – 21 – 8. Note: fa factors as -(A – 4)(A – 2)(A + 1). You don't have to show this. 4 0 0 2 (b) Let D = Find an orthogonal matrix S so that A = SDS". 0 0 Express e in coordinates with respect to the columns of S.
[2 1 4. Let A = 1 1 -1 2 -1 2 Show that the characteristic polynomial fa of A is -X³ + 5A² – 21 – 8. Note: fa factors as -(A – 4)(A – 2)(A + 1). You don't have to show this. 4 0 0 2 (b) Let D = Find an orthogonal matrix S so that A = SDS". 0 0 Express e in coordinates with respect to the columns of S.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 9E
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Transcribed Image Text:1
2
4. Let A = |1
1
-1
-1
2
Show that the characteristic polynomial fa of A is –X3 + 5A² – 21 – 8.
(a)
Note: fa factors as -(A – 4)(A – 2)(A + 1). You don't have to show this.
| 4 0
0 2
(b)
Let D =
. Find an orthogonal matrix S so that A = SDS".
-1
(c)
Express ei in coordinates with respect to the columns of S.
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