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This is the tutorial letter for linear algebra. It describes what the course is all about and what will be covered
Typology: Summaries
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MAT1503/102/0/
10.13 Study Guide Unit 12: Dot Product; Projections, Cross Product, Lines and Planes in 3-Space, and Euclidean n- ..................................................................................................................................................................
1. Contacts of academic staff involved in the module
Lecturers Email Telephone Dr ZI Ali [email protected] 0116709163 Dr Katlego Sebogodi [email protected] 0116709151 Prof Talat Nazir [email protected] 0116709287 Dr PP Ghosh [email protected] Prof A Adem [email protected]
2. Contacts of learner support structures in Unisa
Email Telephone Career Guidance Counselling Academic Literacy
3. Contacts and physical locations of Unisa’ learning centres
LEARNING CENTRES: PHYSICAL ADDRESS CONTACTS: TUTORIAL SERVICES UNISA POLOKWANE, Tutorial Services Office 23A Landros Mare’ Street, Polokwane, 0742
(015) 290 3417 (015) 290- UNISA NELSPRUIT, Tutorial Services Office Standard Bank Centre : 1st Floor , 31 Brown Street, Nelspruit, 1201
(013) 755 2476 UNISA PRETORIA HUB (THUTONG) Tutorial Service Centre Bld 14, Sunnyside Campus, Cnr Walker & Joubert Str., Pretoria 0003
(012) 441 5868 / 5766
UNISA JOHANNESBURG Tutorial Services Office Old JSE Annekes Building 1 Kerk Street, Johannesburg, 2000
(011) 630-
UNISA FLORIDA, Tutorial Services Office, F-Block, Cnr Christiaan de Wet/Pioneer Ave., Florida 0001
(011) 471- UNISA BENONI, 90 General Building, Elston Ave, Benoni, 1501
(011) 421- (011) 421- UNISA DURBAN Tutorial Services Office, Kwazulu Natal 230 Stalwart Simelane Street, Durban, 4001
(031) 332- 2202 (031) 335-1751/ UNISA PIETERMARITZBURG, Tutorial Services Office 1 Langalibalele Str, Pietermaritzburg, 3201
(033) 355- UNISA NEWCASTLE, Tutorial Services Office Cnr Sutherland and Harding Str, Newcastle, 2940
(033) 355- UNISA PAROW, Tutorial Services Office 15 Jean Simonis Street, Parow, 7499
(021) 936- 4146
UNISA MTHATHA, Tutorial Services Office 32 Cnr Victoria & York Rd Str, Economic Affairs Building, Umtata, 5100
(047) 531-5002/ UNISA EAST LONDON Tutorial Services Office, 10 St Lukes Road, Southernwood, East London, 5201
(043) 743 9246
LEARNING CENTRES: PHYSICAL ADDRESS CONTACTS: TUTORIAL SERVICES UNISA PORT ELIZABETH Tutorial Services Office Cnr Hurd Street & 76 5th Avenue Newton Park; Port Elizabeth, 6045
(041) 365 6650/
UNISA MAFIKENG Tutorial Services Office 29 Main Street Opposite ABSA Bank, Mafikeng Mafikeng, 2745
(018) 381-6617/
UNISA RUSTENBURG Tutorial Services Office Forum Building (1st Floor) Cnr. OR Tambo & Steen Street Rustenburg, 0300
(014) 594 8800/
UNISA POTCHEFSTROOM Tutorial Services Office, 20 Auret Street, Potchefstroom, 2531
(018) 294 3362/
UNISA KIMBERLEY Tutorial Services Office Shop 3 – Liberty Life Building, Chapel St, Kimberley, 8301
(053) 832 6391
UNISA BLOEMFONTEIN Tutorial Services Office NRE House, 161 Zastron Street Bloemfontein, 9301
(051) 411-0459/411 0440 (051) 430-4353/411 0452
UNISA KROONSTAD Tutorial Services Office NFS Building 1st floor, 36 Brand Street, Kroonstad, 9500
(056) 213-2053/
Unisa recognizes the importance of tutorials as one way we can provide you with quality teaching to increase your chances of succeeding in your studies. In order to make it easier for you to take advantage of the tutorials, you have the choice of attending tutorials in face-face classes at the learning center, or participating in e- tutoring on myUnisa.
Before you start your tutorials, please read carefully through this Tutorial Resource and through Tutorial Letter 101 for MAT1503. The Tutorial Resource contains the
Your choice to study by distance is commendable because of the many advantages that studying by distance offers to you. However, although studying through distance learning should motivate you to learn to study independently, independent study may not be easy for you. Studying alone can at times be indeed a lonely experience, which may affect your success. This is because in the distance education environment, minimal, yet vital interaction takes place between yourself and your lecturers and between yourself and other students in the same module. This is the main reason why we consider tutorials as a vital element of your learning. Tutorials give you the opportunity to interact with others to exchange knowledge, with guidance by a mentor who understands the subject. You must therefore make every effort to participate in the tutorials.
Please note also that tutors mark your assignments, discuss the feedback with you, and use the formative assessment to help you to prepare for the final examination. Therefore, given also that the assignments contribute 20% to your final mark, it is extremely important that you participate in the tutorials and seize every opportunity to get assistance from the tutor.
Before and during each tutorial, ask yourself the following questions;
In this module, we have given you the choice to attend face-face tutorials which are delivered by a tutor at a learning centre, or to participate in e-tutorials on myUnisa. You can opt for face-face or e-tutoring, or both. However, we strongly recommend that you opt for e-tutoring for the following reasons;
One of the reasons why MAT1503 is offered over a year is to create ample time for you to access tutorials. Tutorials are delivered over a period of 30-40 weeks during the year, depending on the date on which you register for the module (for online tutorials) and on the date on which you enrol for tutorials at a learning centre. Once a tutorial site is created on myUnisa, e-tutorials are open all the time, although the tutor is only live on specific days and times, depending on availability. Depending on the subject content of the tutorial, a tutorial session typically takes approximately 2-3 weeks in an e-tutorial. You can be on the tutorial site myUNISA at any time. However, you are encouraged to maintain a regular presence on myUnisa (even if sometimes you do not do much more than browse through announcements and, or other students’ conversations). The ideal is to spend an average of 2-3 hours per week on myUnisa
This icon draws your attention to some of the most common mistakes around a concept which may be applicable to you. This part of the tutorial assists you to avoid the common mistakes and misconceptions which may slow your learning and may embarrass you as you engage with others
This icon draws your attention to some of the most frequently asked questions around the subject. This part of the tutorial assists you to focus on the subject and stimulates your thinking by looking at the subject from different angles.
This icon draws your attention to important terms and definitions in the subject. This part of the tutorial clarifies the key terms and definitions around the concept.
This icon draws your attention to an open discussion on the main concept of the tutorial. This part of the tutorial is the focal or main activity of the tutorial, where we exchange information and construct new knowledge together.
This icon draws your attention to what you need to do practically, independently or with others in order to understand the concept better? It supports the learning of the concept from its foundations, and its application in relation to other, more complex concepts.
This icon draws your attention to your worksheets so that you can practice for assignments.. This part of the tutorial helps you to see whether or not you are achieving or showing potential to do well in your assignments.
This icon draws your attention to additional reading resources relevant to the tutorial. This part of the tutorial encourages you to read wider around the tutorial content to broaden your understanding of concepts.
This icon draws your attention to a checklist of what you have covered in the tutorials. This part of the tutorial helps you take stock of what you have learnt in the tutorial.
This icon draws your attention to the content of the next tutorial. This part of the tutorial gives you opportunity to prepare for the next tutorial, and also provides continuity in the learning process.
In order for the tutorials to be effective, exciting and meaningful, we all need to follow certain ground rules. Before starting on tutorials, the tutor will ask you to discuss and
agree on a set of rules to be followed by everybody in the group. This is important for the tutorials to be a pleasant and useful experience for everyone. We refer to good behavior in tutorials as netiquette. You must therefore sincerely to commit to the netiquette, and respect it at all times! Misconduct during tutorials can lead to expulsion from the tutorial group.
Share information with others.
Prepare to engage in meaningful discussions with others by prior study around the concept.
Complete all the recommended learning activities within the prescribed times.
Attend 75 % of the face-face tutorials or maintain a regular presence on myUnisa, an average of 3- hours per week
Pose at least three relevant questions in each face-face class or post at least one question or comment in appropriate sites every time I visit the tutorial site on myUnisa
Respect the university policy on communication which, (among other things) encourages the use of appropriate language, courtesy and respect for others.
Focus of the tutorial Actions that describe meaningful participation in the tutorial
Foundation content
Foundation content is meant to refresh the basic knowledge you may need to understand higher concepts. Do not assume you know, read though all the recommended resources and test yourself using the self- assessment exercises. Remember, it is important to read and understand additional resources for you to score high in the journal of tutorial reflections.
Common mistakes misconceptions
Identifying the common mistakes and misconceptions around a concept helps to ensure that everybody in the tutorial group starts off at the same level of understanding. Clearing misconceptions and avoiding common mistakes helps us to narrow discussions to key issues, and thereby accelerate learning. Therefore, before each tutorial, clear your mistakes and any misconceptions using the list provided. Thereafter, be prepared to make other mistakes or expose other misconceptions. Others may in fact share the same, and you can help each other in correcting them.
Frequently asked questions (FAQ)
Identifying the FAQ around a concept similarly helps to ensure the tutorial group starts off at the same level of understanding. Clearing your question against the list of FAQ also saves tutorial time. Before you ask a question, clear it by looking at the FAQ. We encourage you to ask questions in the public domain in the hope that it may help others too. However, questions you may not feel comfortable to ask in an open discussion such as in a face-face class or in the discussions forums on myUnisa can be asked in private consultations with a face-face tutor, or by posting in the Q & A tool on myUnisa.
Discussions
Read around before engaging in a discussion so that you can engage in meaningful conversations with others. In the discussions on myUnisa, posting your own topics [only when invited to open a discussion topic] is a good way to direct the discussion in your favour. Expressing your comments or opinions allows the tutor to identify gaps in your knowledge. The tutor does not always give you a straight answer, but will ask you probing or prompting questions to help you to think through the question. Stay on a discussion until it’s closed by the tutor. Be known as a critical thinker. Remember, it is important for you to make the required minimum number of contributions in each discussion for you to score high in the journal of tutorial reflections.
Assignments & feedback
As a rule, except if they are group activities, assignments are not discussed before the due date, but after. Once the discussion on an assignment is open, look critically at the feedback to your assignments regardless of the mark you get, and ask more questions if necessary. The tutor will always probe your mastery of concepts through more questions.
Self-assessment/ Learning activities
Do as many of the learning activities provided in the tutorials as possible. Do them as well as if you are doing an assignment. This helps the tutor to identify knowledge gaps and to suggest appropriate additional learning activities tailor-made to address your specific needs. Remember, it is important to do the activities diligently for you to score high in the journal of tutorial reflections. Reflection on the tutorial session
Do not go out of a tutorial session with unanswered questions. Use the checklist, and further test your knowledge in the reflective discussions with your peers. Additional (including online) learning resources
Look at all recommended learning resources and take notes. It is important to read and understand all the resources recommended for further reading for you to score high in the journal of tutorial reflections
We believe the tutorials are most meaningful if members of the group all believe in the power of interactive or collaborative learning;
(^1) The Power of Interactive Learning
What I hear, I forget.
What I hear and see, I remember a little.
What I hear, see, and ask questions about or discuss with someone else I begin to understand.
What I hear, see, discuss, and do, I acquire knowledge and skill.
What I teach to another, I master.”
(^1) Silberman, M. 1996. Active learning: 101 Strategies to Teach any Subject. Boston: Allyn and Bacon.
Visit the following link and choose the video that best describe the systems of linear equations:
1. Outcomes: You should be able to - Identify and analyse a linear equation - Find the augmented matrix of a system of linear equations - Determine whether a given sequence of numbers or a given element is a solution of a linear equation (or system of linear equations) - Determine algebraically or geometrically whether a system of linear equations in 2 unknowns has no solution, exactly one solution or infinitely many solutions - State the three elementary row operations - Find the solution of a linear system of equations using elementary row _operations
Basic concepts of system of linear equations in the following websites:
1. Generalize the case where there are three straight lines in the plane defined by three linear equations. What if there are n lines defined _by n equations?
Attempt the following problems: Anton , Exercise Set 1.1, Questions 1, 2, 3, 7, 12, and 14. Pages 20-24 (from e-book, 10th^ Edition).
Test yourself by attempting tutorial- related questions given on the worksheets that you can find in the following webpages:
1. Outcomes: You should be able to - Identify matrices that are in row-echelon form, reduced row-echelon form, or generalized row-echelon form - Solve a linear system by using Gauss-Jordan elimination (i.e. by reducing the augmented matrix to reduced row-echelon form) - Solve a linear system by using Gaussian elimination (i.e. by reducing the augmented matrix to row-echelon form) - Solve a linear system by reducing the augmented matrix to generalized row-echelon form - Determine if/when a linear system has no solution, exactly one solution or infinitely many solutions - Determine if/when a linear system of homogeneous equations has only the trivial solution (i.e. only one solution) or the trivial as well as _nontrivial solutions (i.e. infinitely many solutions).
The Gaussian elimination methods are used for solving systems of linear equations
Attempt the following problems: Anton , Exercise Set 1.2, Questions 15, 19, 23, 27, 28, 29, and 30. Pages 76-77 (from e-book, 10th^ Edition).
Test yourself by attempting tutorial- related questions given on the worksheets that you can find in the following webpages:
The assessment related to this session is Assessment one. See the tutorial letter for details.
