STAT 200 Lecture Notes - Lecture 16: Attractor

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Published on 27 Jul 2020
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Department
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Exam
Name___________________________________
Forthegivenmatrixandeigenvalue,findaneigenvectorcorrespondingtotheeigenvalue.
1) A=-13 2
-40 5 ,λ=-5
A)
-4
1
B)
1
4
C)
1
-4
D)
4
1
1)
2) A=-18 -5
60 17 ,λ=2
A)
1
17
B)
-4
1
C)
1
-4
D)
1
0
2)
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)
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)
Findtheeigenvaluesofthegivenmatrix.
5) -14 -6
36 16
A) -2
,
4B)
-2
,
-4C)
-4D)
-2
5)
1
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6) 56 10
-275 -49
A) 1
,
6B)
-1
,
-6C)
-1D)6
6)
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)
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)
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)
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)
2
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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)
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)
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)
3
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