-10-2 020 A= 26) Find etA, 3041. 11 = A= [] find etA. A₁ = -1, multiplicity of 2, A3=1. X=-1: Av=-Av -x+y+22= -x 1 Y=0 -y+42=-y-y=-y 2=-2,2=0 V₁ = (ó). Since only 1 eigenvector on d- multiplicity 2, A is not diagonalizable. Find V2: (A+IPV=0 0121/012/X 004 004 049 = 002/1002112, Let V₂ = (?). Find V3: =1, Av=AV 008 004 = 0. -x+y+22=x, 22=2x-y -Y+42=4, 22=y L& V3 = (3). 2=2. 102 P-1=/09: P-1 101-2 Then P= (P= (27). 10011. 2011, S = P(-2-10/P-1 S = 1/2-14 N = A-S = / 01-3 000 etAt(S+N) -ets, etN = to = ets.etN = P(0² = + 0) P₁1 [I+ + N + 1 ² N²] 012 et/ 1102 let 0,0 10-217-2 。 eto 01-20 001/o o etoo 1/100 e • 2et t 2et 0 et 11 t = 21-21 0 1 a -2 00 1 0 et tēt ēt (-24-2) + 2et et = PtA t tet 20+ + 2et 0 et
-10-2 020 A= 26) Find etA, 3041. 11 = A= [] find etA. A₁ = -1, multiplicity of 2, A3=1. X=-1: Av=-Av -x+y+22= -x 1 Y=0 -y+42=-y-y=-y 2=-2,2=0 V₁ = (ó). Since only 1 eigenvector on d- multiplicity 2, A is not diagonalizable. Find V2: (A+IPV=0 0121/012/X 004 004 049 = 002/1002112, Let V₂ = (?). Find V3: =1, Av=AV 008 004 = 0. -x+y+22=x, 22=2x-y -Y+42=4, 22=y L& V3 = (3). 2=2. 102 P-1=/09: P-1 101-2 Then P= (P= (27). 10011. 2011, S = P(-2-10/P-1 S = 1/2-14 N = A-S = / 01-3 000 etAt(S+N) -ets, etN = to = ets.etN = P(0² = + 0) P₁1 [I+ + N + 1 ² N²] 012 et/ 1102 let 0,0 10-217-2 。 eto 01-20 001/o o etoo 1/100 e • 2et t 2et 0 et 11 t = 21-21 0 1 a -2 00 1 0 et tēt ēt (-24-2) + 2et et = PtA t tet 20+ + 2et 0 et
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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Could you solve the problem completely using
Transcribed Image Text:-10-2
020
A= 26) Find etA,
3041.
![11
=
A= [] find etA.
A₁ = -1, multiplicity of 2, A3=1.
X=-1: Av=-Av
-x+y+22= -x 1 Y=0
-y+42=-y-y=-y
2=-2,2=0
V₁ = (ó).
Since only 1 eigenvector on d- multiplicity 2, A is not diagonalizable.
Find V2: (A+IPV=0
0121/012/X
004 004
049 =
002/1002112,
Let V₂ = (?).
Find V3: =1, Av=AV
008
004
= 0.
-x+y+22=x, 22=2x-y
-Y+42=4, 22=y
L& V3 = (3).
2=2.
102 P-1=/09:
P-1 101-2
Then P= (P= (27).
10011.
2011,
S = P(-2-10/P-1 S = 1/2-14
N = A-S = / 01-3
000
etAt(S+N) -ets, etN
=
to
=
ets.etN
= P(0² = + 0) P₁1 [I+ + N + 1 ² N²]
012
et/
1102 let 0,0 10-217-2
。 eto 01-20
001/o o etoo 1/100
e
• 2et
t
2et
0
et
11 t = 21-21
0 1
a
-2
00 1
0
et
tēt
ēt (-24-2) + 2et
et = PtA
t
tet 20+ + 2et
0
et](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe742bcfc-6571-4eb6-8020-0d244ddd1492%2F1571cc1a-e7ca-4c6f-bec5-8fcb2c9cdbac%2Ftheu7j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11
=
A= [] find etA.
A₁ = -1, multiplicity of 2, A3=1.
X=-1: Av=-Av
-x+y+22= -x 1 Y=0
-y+42=-y-y=-y
2=-2,2=0
V₁ = (ó).
Since only 1 eigenvector on d- multiplicity 2, A is not diagonalizable.
Find V2: (A+IPV=0
0121/012/X
004 004
049 =
002/1002112,
Let V₂ = (?).
Find V3: =1, Av=AV
008
004
= 0.
-x+y+22=x, 22=2x-y
-Y+42=4, 22=y
L& V3 = (3).
2=2.
102 P-1=/09:
P-1 101-2
Then P= (P= (27).
10011.
2011,
S = P(-2-10/P-1 S = 1/2-14
N = A-S = / 01-3
000
etAt(S+N) -ets, etN
=
to
=
ets.etN
= P(0² = + 0) P₁1 [I+ + N + 1 ² N²]
012
et/
1102 let 0,0 10-217-2
。 eto 01-20
001/o o etoo 1/100
e
• 2et
t
2et
0
et
11 t = 21-21
0 1
a
-2
00 1
0
et
tēt
ēt (-24-2) + 2et
et = PtA
t
tet 20+ + 2et
0
et
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