COLLIN COUNTY COMMUNITY COLLEGE COURSE SYLLABUS CREDIT HOURS: 3 LECTURE HOURS: 3 LAB HOURS: 0
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1 COLLIN COUNTY COMMUNITY COLLEGE COURSE SYLLABUS Revised Fall 2017 COURSE NUMBER: MATH 2318 COURSE TITLE: Liear Algebra CREDIT HOURS: 3 LECTURE HOURS: 3 LAB HOURS: 0 ASSESSMENTS: Noe PREREQUISITE: MATH 2414 or MATH 2419 COREQUISITE: Noe COURSE DESCRIPTION: Itroduces ad provides models for applicatio of the cocepts of vector algebra. Topics iclude fiite dimesioal vector spaces ad their geometric sigificace; represetig ad solvig systems of liear equatios usig multiple methods, icludig Gaussia elimiatio ad matrix iversio; matrices; determiats; liear trasformatios; quadratic forms; eigevalues ad eigevector; ad applicatios i sciece ad egieerig. TEXTBOOK: Elemetary Liear Algebra, 8 th editio, by Ro Larso 2017, Cegage Learig SUPPLIES: Graphig calculator required STUDENT LEARNING OUTCOMES: Upo successful completio of this course, studets will: 1. Be able to solve systems of liear equatios usig multiple methods, icludig Gaussia elimiatio ad matrix iversio. (EQ) 2. Be able to carry out matrix operatios, icludig iverses ad determiats. (EQ) 3. Demostrate uderstadig of the cocepts of vector space ad subspace. (CS) 4. Demostrate uderstadig of liear idepedece, spa, ad basis. (CT/CS) 5. Be able to determie eigevalues ad eigevectors ad solve problems ivolvig eigevalues. (EQ) 6. Apply priciples of matrix algebra to liear trasformatios. (CT) 7. Demostrate applicatio of ier products ad associated orms. (CS) COURSE REQUIREMENTS: Attedig lectures, completig assigmets ad exams. COURSE FORMAT: Lecture ad guided practice. METHOD OF EVALUATION: A miimum of four proctored exams ad a proctored comprehesive fial exam will be give. Homework ad/or quizzes may be used i place of oe exam or i additio to exams. The weight of each of these compoets of evaluatio will be MATH
2 specified i the idividual istructor s addedum to this syllabus. All out-of-class course credit, icludig home assigmets, service-learig, etc. may ot exceed 25% of the total course grade; thus, at least 75% of a studet s grade must cosist of proctored exams, ad o studet may retake ay of these exams. ATTENDANCE POLICY: Attedace is expected of all studets. If a studet is uable to atted, it is his/her resposibility to cotact the istructor to obtai assigmets. Please see the schedule of classes for the last day to withdraw from the course with a grade of W. RELIGIOUS HOLY DAYS: I accordace with sectio of the Texas Educatio Code, the college will allow a studet who is abset from class for the observace of a religious holy day to take a examiatio or complete a assigmet scheduled for that day withi a reasoable time. A copy of the state rules ad procedures regardig holy days ad the form for otificatio of absece from each class uder this provisio are available from the Admissios ad Records Office. Please refer to the curret Colli Studet Hadbook. ADA STATEMENT: Colli College will adhere to all applicable federal, state ad local laws, regulatios ad guidelies with respect to providig reasoable accommodatios as required to afford equal educatioal opportuity. It is the studet's resposibility to cotact the ACCESS Office, SCC-D140 or , (V/TDD ) to arrage for appropriate accommodatios. See the curret Colli studet Hadbook for additioal iformatio. ACADEMIC ETHICS: Please see sectio of the Colli Studet Hadbook. Cotact the Dea of Studets at for the studet discipliary process ad procedures. COURSE CONTENT: Proofs ad derivatios will be assiged at the discretio of the istructor. The studet will be resposible for kowig all defiitio ad statemets of theorems for each sectio outlied i the followig modules. MODULE 1: Systems of Liear Equatios, Matrices, Determiats The studet will be able to: 1. Recogize a liear equatio i variables. 2. Fid a parametric represetatio of a solutio set. 3. Determie whether a system of liear equatios is cosistet or icosistet. 4. Use back-substitutio ad Gaussia elimiatio to solve a system of liear equatios. 5. Determie the size of a matrix ad write a augmeted or coefficiet matrix from a system of liear equatios. 6. Use matrices ad Gaussia elimiatio with back-substitutio to solve a system of liear equatios. 7. Use matrices ad Gauss-Jorda elimiatio to solve a system of liear equatios. 8. Solve a homogeeous system of liear equatios. 9. Set up ad solve a system of equatios to fit a polyomial fuctio to a set of data poits, as well as to represet a etwork. 10. Add, subtract matrices ad multiply a matrix by a scalar. MATH
3 11. Multiply two matrices. 12. Use matrices to solve a system of liear equatios. 13. Use properties of matrix operatios to solve matrix equatios. 14. Fid the traspose of a matrix, the iverse of a matrix (if it exists). 15. Use a iverse matrix to solve a system of liear equatios. 16. Factor a matrix ito a product of elemetary matrices. 17. Fid ad use a LU-factorizatio of a matrix to solve a system of liear equatios. 18. Use a stochastic matrix to measure cosumer preferece (optioal). 19. Use matrix multiplicatio to ecode ad decode messages. 20. Use matrix algebra to aalyze Leotief iput-output models (optioal). 21. Use the method of least squares to fid the least squares regressio lie for a set of data (optioal). 22. Fid the determiats of a 2 x 2 matrix ad a triagular matrix. 23. Fid the miors ad cofactors of a matrix ad use expasio by cofactors to fid the determiat of a matrix. 24. Use elemetary row ad colum operatios to evaluate the determiat of a matrix. 25. Recogize coditios that yield zero determiats. 26. Fid the determiat of a matrix product ad a scalar multiple of a matrix. 27. Fid the determiat of a iverse matrix ad recogize equivalet coditios for a osigular matrix. 28. Fid the determiat of the traspose of a matrix. 29. Fid the adjoit of a matrix ad use it to fid its iverse. 30. Use Cramer's Rule to solve a system of liear equatios. 31. Use determiats to fid the area, volume, ad the equatios of lies ad plaes. MODULE 2: Vector Spaces, Ier Product Spaces The studet will be able to: 1. Represet a vector as a directed lie segmet Perform basic vector operatios i R. 3. Perform basic vector operatios i R. 4. Write a vector as a liear combiatio of other vectors. 5. Defie a vector space ad recogize some importat vector spaces. 6. Show that a give set is ot a vector space. 7. Determie whether a subset W of a vector space V is a subspace of V. 8. Determie subspaces of R. 9. Write a liear combiatio of a set of vectors i a vector space V. 10. Determie whether a set S of vectors i a vector space V is a spaig set of V. 11. Determie whether a set of vectors i a vector space V is liearly idepedet. 12. Recogize bases i the vector spaces R, M m,, ad P. 13. Fid the dimesio of a vector space. 14. Fid a basis for the row, a basis for the colum space, ad the rak of a matrix. 15. Fid the ullspace of a matrix. 16. Fid the solutio of a cosistet system Ax b i the form xp x h. MATH
4 17. Fid a coordiate matrix relative to a basis i R. 18. Fid the trasitio matrix from the basis B to the basis B i R. 19. Represet coordiates i geeral -dimesioal spaces. 20. Determie whether a fuctio is a solutio of a differetial equatio ad fid the geeral solutio of a give differetial equatio. 21. Use the Wroskia to test a set of solutios of a liear homogeeous differetial equatio for liear idepedece (optioal). 22. Idetify ad sketch the graph of a coic or degeerate coic sectio ad perform a rotatio of axes (optioal). 23. Fid the legth of a vector ad fid a uit vector. 24. Fid the distace betwee two vectors. 25. Fid a dot product ad the agle betwee two vectors, determie orthogoality ad verify the Cauchy-Schwarz Iequality, the triagle iequality, ad the Pythagorea Theorem. 26. Determie whether a fuctio defies a ier product, ad fid the ier product of two vectors i R, M m,, P ad Cab [, ]. 27. Fid a orthogoal projectio of a vector oto aother vector i a ier product space. 28. Show that a set of vectors is orthogoal ad forms a orthoormal basis, ad represet a vector relative to a orthoormal basis. 29. Apply the Gram-Schmidt orthoormalizatio process Fid the cross product of two vectors i R (optioal). 31. Fid the liear or quadratic least squares approximatio of a fuctio (optioal). 32. Fid the th-order Fourier approximatio of a fuctio (optioal). MODULE 3: Liear Trasformatios, Eigevalues ad Eigevectors The studet will be able to: 1. Fid the image ad preimage of a fuctio. 2. Show that a fuctio is a liear trasformatio, ad fid a liear trasformatio. 3. Fid the kerel of a liear trasformatio. 4. Fid a basis for the rage, the rak, ad the ullity of a liear trasformatio. 5. Determie whether a liear trasformatio is oe-to-oe or oto. 6. Determie whether two vector spaces are isomorphic. 7. Fid the stadard matrix for a liear trasformatio. 8. Fid the stadard matrix for the compositio of a liear trasformatios ad fid the iverse of a ivertible liear trasformatio. 9. Fid the matrix for a liear trasformatio relative to a ostadard basis. 10. Fid ad use a matrix for a liear trasformatio. 11. Show that two matrices are similar ad use the properties of similar matrices. 12. Idetify liear trasformatios defied by reflectios, expasios, cotractios, or shears 2 i R (optioal) Use a liear trasformatio to rotate a figure i R (optioal). 14. Verify eigevalues ad correspodig eigevectors. 15. Fid the eigevalues ad correspodig eigespaces. 16. Use the characteristic equatio to fid eigevalues ad eigevectors, ad fid the MATH
5 eigevalues ad eigevectors of triagular matrix. 17. Fid the eigevalues of similar matrices, determie whether a matrix is diagoalizable, 1 ad fid a matrix P such that P AP is diagoal. 18. Fid, for a liear trasformatio T : V V, a basis B for V such that the matrix for T relative to B is diagoal. 19. Recogize, ad apply properties of symmetric ad orthogoal matrices. 20. Fid a orthogoal matrix P that orthogoally diagoalizes a symmetric matrix A. 21. Use a matrix equatio to solve a system of first-order liear differetial equatios (optioal). 22. Fid the matrix of quadratic form ad use the Pricipal Axes Theorem to perform a rotatio of axes for a coic ad a quadratic surface (optioal). 23. Solve a costraied optimizatio problem (optioal). MATH
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