# STAT 200 Quiz: Untitled8

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Writeyasanaffinecombinationoftheotherpointslisted.
1) v1=3
-2,v2=1
-1,v3=9
-1,y=7
4
A) y=v1-2v2+2v3B) y= -5v1+4v2+2v3
C) y=4v1-2v2-v3D) y=3v1+3v2-5v3
1)
2) v1=
1
1
2
,v2=
0
4
-2
,v3=
1
-5
1
,y=
5
-23
16
A) y=3v1-4v2+2v3B) y= -3v1-2v2+6v3
C) y=2v1+3v2-4v3D) y=7v1+3v2-4v3
2)
DetermineifthevectorpisinSpanSoraffS.
3) Letv1=
2
1
3
-2
,v2=
3
-1
0
4
,v3=
5
4
-1
-2
,p=
5
-3
5
3
,andS={v1,v2,v3}.ItcanbeshownthatSislinearly
independent.
A) pspanSandpaffSB)
pspanSandpaffS
C) pspanSandpaffSD)
pspanSandpaffS
3)
4) Letv1=
2
1
3
-2
,v2=
3
-1
0
4
,v3=
5
4
-1
-2
,p=
10
12
-6
-8
,andS={v1,v2,v3}.ItcanbeshownthatSislinearly
independent.
A) pspanSandpaffSB)
pspanSandpaffS
C) pspanSandpaffSD)
pspanSandpaffS
4)
5) Letv1=
2
1
3
-2
,v2=
3
-1
0
4
,v3=
5
4
-1
-2
,p=
2
-3
7
2
,andS={v1,v2,v3}.ItcanbeshownthatSislinearly
independent.
A) pspanSandpaffSB)
pspanSandpaffS
C) pspanSandpaffSD)
pspanSandpaffS
5)
1
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Provideanappropriateresponse.
6) Whichofthefollowingstatementsaretrue?
I:2v1+2v2-3v3isanaffinecombinationofthe3vectors.
II:Theaffinehulloftwodistinctpointsisaplane.
III:IfS={x},thenaffS={x}.
IV:Ifasetofvectorsinnislinearlyindependent,theneveryvectorinncanbewrittenasan
affinecombinationofthesevectors.
A) IIandIV B) IandII C) IandIII D) I,III,andIV
6)
7) Suppose{v1,v2,v3}isabasisfor3.Whichofthefollowingstatementsaretrue?
I:Span{v2-v1,v3-v1}isaplanein3.
II:Aff{v1,v2,v3}istheplanethroughv1,v2,andv3.
A) II B) I C) BothIandII D) NeitherIorII
7)
8) v1=
2
2
5
,v2=
2
3
-1
,v3=
2
4
3
andS={v1,v2,v3}.AffSisaplanein3.Giveitsequation.
A) 13x+14y=17 B) x=2C)x+y+z=0D)6x+9y+7z=0
8)
9) PickasetSoffourdistinctpointsin3suchthataffSistheplane2x1+x2-3x3=14.
A) S=
2
1
-3
,
4
2
-6
,
0
14
0
,
1
15
1
B) S=
0
17
1
,
1
9
-1
,
-2
18
0
,
0
14
0
C) S=
2
15
1
,
-1
9
-1
,
3
10
0
,
0
0
0
D) S=
0
11
1
,
1
9
1
,
2
18
0
,
0
14
0
9)
10) Whichofthefollowingstatementsaretrue?
I:Supposef:nmisalineartransformationandSisanaffinesubsetofn.Itfollowsthat
thesetofimagesf(S)isanaffinesubsetofm.
II:IfAB,thenaffAB.
A) I B) NeitherIorII C) BothIandII D) II
10)
11) [(affA)(affB)](AB)
Whatpropertymusttheset(AB)haveiftheabovestatementistrue?
B) (AB)mustcontaincollinearpoints.
C) ABsothat(AB)=A.
D) (AB)hastobeaffine.
11)
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Determineifthesetofpointsisaffinelydependent.Ifso,constructanaffinedependencerelationforthepoints.
12) 4
8,8
4,5
7
A) Thesetisaffinelydependent.34
8
-8
4
+45
7
=0
0
B) Thesetisaffinelyindependent.
C) Thesetisaffinelydependent.31
2
+2
1
-5
7
=0
0
D) Thesetisaffinelydependent.34
8
+8
4
-45
7
=0
0
12)
13)
4
8
-1
,
-8
-16
4
,
0
1
12
,
-16
-31
22
A) Thesetisaffinelydependent.2
4
8
-1
-3
-8
-16
4
-
0
1
12
+
-16
-31
22
=
0
0
0
B) Thesetisaffinelydependent.5
4
8
-1
-3
-8
-16
4
-
0
1
12
-
-16
-31
22
=
0
0
0
C) Thesetisaffinelydependent.2
4
8
-1
+3
-8
-16
4
+
0
1
12
-
-16
-31
22
=
0
0
0
D) Thesetisaffinelyindependent.
13)
Findthebarycentriccoordinatesofpwithrespecttotheaffinelyindependentsetofpointsthatprecedesit.
14)
1
-1
2
1
,
2
1
0
1
,
1
2
-2
0
,p=
-1
-11
14
3
A) (4
,
-1
,
-2) B) (5
,
0,-4) C) (5
,
-2
,
-2) D) (2
,
-2
,
1)
14)
15) 1
1,3
5,0
6,p=2
3
A) (-9,3,7) B) 1
2,0,1
2C) 1
2,1
2,0 D) 2,1
,
-2
15)
16) WhichofthefollowingstatementsaretrueforthesetS={v1,...,vk}inn?
I:{v2-v1,...,vk-v1}islinearlydependentifandonlyifSisaffinelydependent.
II:IfSisaffinelyindependentandapointpinnhasallpositivebarycentriccoordinates
determinedbyS,thenpisnotinaffS.
A) I B) II C) NeitherIorII D) BothIandII
16)
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