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7/31/2019 Math230 Pe Feb2010 Final (2)
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School of AdvancedTechnologies
and Mathematics
Practice Exam
MATH 230Linear Algebra
7/31/2019 Math230 Pe Feb2010 Final (2)
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7/31/2019 Math230 Pe Feb2010 Final (2)
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MATH 230: Linear Algebra 109
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Practice Exam
Theformatofthispracticeexamissimilartothatofyourfinalexam.Foryourown
benefit,youshouldnotlookatthisexamuntilyouhavecompletedyourreviewofthe
course
and
have
submitted
and
received
feedback
on
all
assignments.
When
you
writethisexam,youshouldisolateyourselfforthreehours.Bysimulatingexam
conditionsinthisway,youwilllearnhowtomanageyourtimeonthefinal.Also
rememberthatthefinalexamisclosedbook.
ThePracticeExamAnswerKeyfoundonthepagesimmediatelyfollowingthis
examshouldprovidesufficientinformationtoindicatewhichconceptsyoumay
haveforgottenorneverreallylearned.Whenyouhavecompletedyourreviewofthe
exam,contactyourtutortodiscussanypointsofconcern.
Thenextpagescontaintheselfadministeredfinalexamandtheguideformarking
it.
DONOTturnthepageuntilyouarereadytotrytheexam!
7/31/2019 Math230 Pe Feb2010 Final (2)
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7/31/2019 Math230 Pe Feb2010 Final (2)
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MATH 230: Linear Algebra 111
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THOMPSON RIVERS UNIVERSITY,OPEN LEARNING
MATH 230 LINEAR ALGEBRA
PRACTICE EXAMINATION
Time Allowed: 3 Hours
Total Pages (Including This Page): 5
Total Marks: 100
Materials/Equipment Permitted:
ScientificCalculator
Materials Provided:
Twoexam
answer
booklets
Student: Please Complete This SectionPrint
Clearly.
Surname
_________________________________________
FirstName
_________________________________________
StudentNumber(ninedigits)
_________________________________________
TutorsName
_________________________________________
StudentsSignature(required)
_________________________________________
Date
_________________________________________
Tutor: Please Complete This Section
Print Clearly.
StudentsMark________%
TutorsName
_________________________________
TutorsI.D.No.
_________________________________
TutorsSignature
_________________________________
Date
_________________________________
Instructions
Placeyourphotoidentification(e.g.,driverslicence),examinationconfirmationletter,
ontheupperrighthandcornerofyourdeskforinspectionbytheinvigilator.
Writeyouranswersandcompletesolutionsintheexamanswerbookletsprovided.
Whenyouhavefinished,RETURNALLPAPERS,INCLUDINGTHEEXAMANDALLANSWERBOOKLETS(USEDANDUNUSED)INTHEENVELOPE.FailuretodosomayresultinaFAILgrade.
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112 Practice Exam
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ExamInstructions AttemptALLtenquestions.Eachquestionisworth10marks. Givecompleteanddetailedsolutionstoallproblems.Marksmaybededucted
forinsufficient
details.
Identifyallrow(orcolumn)operationsusedonmatrices.
Unitsmustbegiveninthefinalanswerofanapplication,whereapplicable.
1. UsetheGaussJordanEliminationMethodtofindthecurrents 1I , 2I and 3I forthe
electricalnetwork
shown
below,
where
1 2 1 2 33 volts, 4 volts, 4 , 3 , 1V V R ohms R ohms R ohm= = = = =
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MATH 230: Linear Algebra 113
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2. a. IfAisanidempotentmatrix(thatis, )2 ,A A=
thenprovethat 0)Adet( = or
det( ) 1.A =
b.
Determine
if
the
matrix
B
below
is
diagonalizable.
1 0 0
0 1 1
0 1 1
B
=
3. Considerthefollowingsystemoflinearequations:
( )2
2 5
3 2 20
4 3 24 20
x y z
x y z
x y k k
=
+ =
+ = +
Forwhatvalue(s)ofkdoesthissystemhave:
a. Aninfinitenumberofsolutions?
b. Auniquesolution?
c. Nosolution?
4. IfAisaninvertiblematrix,provethat:
a. ( ) ( )1
1T
TA A
=
b. If AC AB, then C B.= =
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114 Practice Exam
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5. Giventhematrix
=
24
910A
a. Showthat
=4
6v
isaneigenvectorforAandfindthe
correspondingeigenvalue.
b.Calculate 3A u , where 12 .8
=
u
6. Let ( ) ( ){ }0, 2 , 2 , 1, 0, 2B = beabasisforasubspaceof 3R ,andlet( )2,4,1 =x beavectorinthesubspace.
a. Findthecoordinatesofx relativetoB.b. UsetheGramSchmidtOrthonormalizationprocessto
transformBintoanorthonormalset /B .7. Determinewhetherthefunction: ( ) ( )21212122 ,2,,: xxxxxxTRRT += is
alineartransformation.Ifitis,finditsstandardmatrixA.
8. ThelineartransformationTisgivenby ( ) vv AT = ,where1 2
1 0 .
1 1
A
=
Find:
a. AbasisforthekernelofTb. AbasisfortherangeofTc. TherankofTd. ThenullityofT
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MATH 230: Linear Algebra 115
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9. Determinewhether { }20 1 2 0 1 2: 0S a a x a x a a a= + + + + = isasubspaceofP2.
10.Suppose , 2 31 1 2 2 3 3
u v u v u v u v= + + representsaninnerproducton 3R .For
( ) ( )2, 1,1 and 2,4,0u v= =
a. Findtheinnerproductofuandv
b. Findthe
distance
between
uand
v
c. VerifyTheTriangleInequalityforuandv: u v u v
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