For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A = (-108/₂2 -=-1-2/ ·1.8 -0.8

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 7E
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For the following matrices A,
Computo AT. If A is a 2x2 matrix
with real, different eigenvalues,
draw the phase portraits.
a) A₂= /-1.8 -0.8°
a) A= (
-1.2
-0.2
Transcribed Image Text:For the following matrices A, Computo AT. If A is a 2x2 matrix with real, different eigenvalues, draw the phase portraits. a) A₂= /-1.8 -0.8° a) A= ( -1.2 -0.2
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Now,
e
At
2₁ = -19
The coresponding eigen vectors are,
+1 (1)
22-
₂² (1)
Hence, the matrix exponential should be:
et
1) (( ²² e+)(
et
(1
Cette
。
6
22
the
L
e-t
et - 16e-t
-et-ge-t.
2
5/
(C)
(1
4
- e² + 4e-t
et tet
-1
Since the eigen values are
1₁= -1 and 1₂ = -2
shouldn't
e At = VOV¹
v@v-
3 (= + (-26) ?
Transcribed Image Text:Now, e At 2₁ = -19 The coresponding eigen vectors are, +1 (1) 22- ₂² (1) Hence, the matrix exponential should be: et 1) (( ²² e+)( et (1 Cette 。 6 22 the L e-t et - 16e-t -et-ge-t. 2 5/ (C) (1 4 - e² + 4e-t et tet -1 Since the eigen values are 1₁= -1 and 1₂ = -2 shouldn't e At = VOV¹ v@v- 3 (= + (-26) ?
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