STAT 200 Lecture Notes - Lecture 16: Attractor

48 views8 pages
Published on 27 Jul 2020
School
Department
Course
Professor
Exam
Name___________________________________
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Forthegivenmatrixandeigenvalue,findaneigenvectorcorrespondingtotheeigenvalue.
1) A=-13 2
-40 5 ,λ=-5
A)
-4
1
B)
1
4
C)
1
-4
D)
4
1
1)
Answer: B
2) A=-18 -5
60 17 ,λ=2
A)
1
17
B)
-4
1
C)
1
-4
D)
1
0
2)
Answer: C
ForthegivenmatrixA,findabasisforthecorrespondingeigenspaceforthegiveneigenvalue.
3) A=
166
61
-6
-6613
,λ=7
A)
1
0
1
,
0
1
-1
B)
1
0
-1
,
0
1
1
C)
0
1
-1
D)
1
0
-1
3)
Answer: A
4) A=
-400
-10 6 0
-30 16 -2
,λ=-4
A)
1
-1
-7
B)
1
1
0
,
1
0
-7
C)
1
1
7
D)
1
1
0
,
1
0
7
4)
Answer: C
Findtheeigenvaluesofthegivenmatrix.
5) -14 -6
36 16
A) -2
,
4B)
-2
,
-4C)
-4D)
-2
5)
Answer: A
1
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in
6) 56 10
-275 -49
A) 1
,
6B)
-1
,
-6C)
-1D)6
6)
Answer: A
Findthecharacteristicequationofthegivenmatrix.
7) A=
9643
07
-68
0059
0009
A) (9-λ)2(7-λ)(5-λ)=0B)(9
-
λ
)(6 -
λ
)(4 -
λ
)(3 -λ)=0
C) (9-λ)(7-λ)(5-λ)=0D)(9
-
λ
)(9 -
λ
)(8 -
λ
)(3 -λ)=0
7)
Answer: A
8) A=
8-152
031
-1
00
-6-6
000
-5
A) (8-λ)(3-λ)(-6-λ)(-5-λ)=0B)(8
-
λ
)(-1-
λ
)(5 -
λ
)(2 -λ)=0
C) (-5-λ)(-6-λ)(-1-λ)(2-λ)=0D)(2
-
λ
)(-1-
λ
)(-6-
λ
)(-5-λ)=0
8)
Answer: A
Thecharacteristicpolynomialofa5×5matrixisgivenbelow.Findtheeigenvaluesandtheirmultiplicities.
9) λ5+17λ4+72λ3
A) 0(multiplicity1),8(multiplicity1),9 (multiplicity1)
B) 0(multiplicity1),-9(multiplicity1),-8 (multiplicity1)
C) 0(multiplicity3),8(multiplicity1),9 (multiplicity1)
D) 0(multiplicity3),-9(multiplicity1),-8 (multiplicity1)
9)
Answer: D
10) λ5-24λ4+189λ3-486λ2
A) 0(multiplicity2),9(multiplicity2),6 (multiplicity1)
B) 0(multiplicity2),-9(multiplicity2),-6 (multiplicity1)
C) 0(multiplicity2),-9(multiplicity2),6 (multiplicity1)
D) 0(multiplicity1),9(multiplicity3),6 (multiplicity1)
10)
Answer: A
2
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in
FindaformulaforAk,giventhatA=PDP-1,wherePandDaregivenbelow.
11) A=-19
-614 ,P=31
21 ,D=50
08
A)
3·5k-2·8k3·8k-3·5k
2·5k-2·8k3·8k-2·5k
B)
3·5k+2·8k3·8k+3·5k
2·5k+2·8k3·8k+2·5k
C)
5k0
08k
D)
3·5k-2·8k3·8k+3·5k
2·5k+2·8k3·8k-2·5k
11)
Answer: A
DiagonalizethematrixA,ifpossible.Thatis,findaninvertiblematrixPandadiagonalmatrixDsuchthat A=PDP-1.
12) A=
-11 3-9
0-50
6-34
A)
P=
15-1
530
131
,D=
-510
0-50
00-2
B)
P=
10-1
530
111
,D=
-500
0-50
00-2
C)
P=
10-1
030
111
,D=
-500
010
00-2
D)
P=
10-1
530
111
,D=
-50-2
0-50
0-5-2
12)
Answer: B
13) A=
200
120
002
A)
P=
100
220
011
,D=
210
020
002
B)
P=
10-1
220
111
,D=
201
121
002
C) Notdiagonalizable D)
P=
121
021
-101
,D=
200
020
002
13)
Answer: C
3
Unlock document

This preview shows pages 1-3 of the document.
Unlock all 8 pages and 3 million more documents.

Already have an account? Log in

Get OneClass Grade+

Unlimited access to all notes and study guides.

Grade+All Inclusive
$10 USD/m
This Study Guide
$25 USD
You will be charged $120 USD upfront and auto renewed at the end of each cycle. You may cancel anytime under Payment Settings. For more information, see our Terms and Privacy.
Payments are encrypted using 256-bit SSL. Powered by Stripe.