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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD THAT HAS PASSED THE END DATE: 

Use and apply matrices and graphs to solve systems of equations and network problems 
SAQA US ID UNIT STANDARD TITLE
243840  Use and apply matrices and graphs to solve systems of equations and network problems 
ORIGINATOR
SGB Math Literacy, Math, Math Sciences L 2 -4 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY
-  
FIELD SUBFIELD
Field 10 - Physical, Mathematical, Computer and Life Sciences Mathematical Sciences 
ABET BAND UNIT STANDARD TYPE PRE-2009 NQF LEVEL NQF LEVEL CREDITS
Undefined  Regular-Fundamental  Level 5  Level TBA: Pre-2009 was L5  2 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2018-07-01  2023-06-30  SAQA 06120/18 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2024-06-30   2027-06-30  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This unit standard does not replace any other unit standard and is not replaced by any other unit standard. 

PURPOSE OF THE UNIT STANDARD 
To help learners represent data and position in the three-dimensional world by means of matrices and graphs.

A person credited with this unit standard is able to:
  • Solve systems of linear equations by diagonalisation or determining the inverse matrix.
  • Use graphs and simple algorithms to solve network problems.
  • Use matrices to represent and solve travel problems.

    In order to see this unit standard with its exact formulae, please use the link at the end of the Searchable Database home page. SAQA is in the process of adapting the National Learners' Records Database to accommodate such formulae. 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
  • Mathematics at NQF Level 4. 
    		•

    UNIT STANDARD RANGE 
    N/A 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Solve systems of linear equations by diagonalisation or determining the inverse matrix. 
    OUTCOME RANGE 
    Systems of linear equations are in three variables. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Systems of linear equations in three variables are solved by diagonalisation through row reduction. 

    ASSESSMENT CRITERION 2 
    The inverse of a 3 x 3 matrix can be found by a sequence of row transformations using the formula shown in the MS Word document. 

    ASSESSMENT CRITERION 3 
    The determinant of a 3 x 3 matrix is correctly calculated. 

    ASSESSMENT CRITERION 4 
    The inverse matrix is used to solve systems of linear equations. 

    SPECIFIC OUTCOME 2 
    Use graphs and simple algorithms to solve network problems. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Minimum connector problems are solved using graphs and algorithms. 
    ASSESSMENT CRITERION RANGE 
    Algorithms include the Kruskal and Prim algorithms.
     

    ASSESSMENT CRITERION 2 
    Travelling salesman problems may be solved using graphs and simple algorithms in the literature. 

    SPECIFIC OUTCOME 3 
    Use matrices to represent and solve travel problems. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Adjacency matrices are used to represent network problems. 

    ASSESSMENT CRITERION 2 
    Adjacency matrices are used to solve network optimisation problems. 
    ASSESSMENT CRITERION RANGE 
    Network problems include shortest path, Chinese postman, minimum connector and travelling salesmen roblems.
     

    ASSESSMENT CRITERION 3 
    Minimum connector problems may be solved using matrices and algorithms. 
    ASSESSMENT CRITERION RANGE 
    Algorithms include the Kruskal and Prim algorithms.
     

    ASSESSMENT CRITERION 4 
    Travelling salesman problems may be solved using matrices and simple algorithms in the literature. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
  • The assessment will be governed by the policies and guidelines of the relevant Education and Training Quality Assuror (ETQA) that has jurisdiction over this field of learning.
  • The assessor will be accredited, have the competence of this unit standard and be a subject matter expert in this learning area. 
    		•

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
  • The solution of systems of three variable linear equations by the method of diagonalisation.
  • Finding the inverse of 3 x 3 matrices by a sequence of row transformations.
  • Calculate the determinant of a 3 x 3 matrix.
  • Use graphs, matrices and simple algorithms to solve travel problems.
  • Solve minimum connector and travelling salesman problems using techniques learned in this course. 
    		•

    UNIT STANDARD DEVELOPMENTAL OUTCOME 
    N/A 

    UNIT STANDARD LINKAGES 
    N/A 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Identifying and solving problems in which responses display that responsible decisions using critical and creative thinking have been made when:
  • Solving a variety of mathematical problems requiring graphs and matrices. 
    		•

    UNIT STANDARD CCFO WORKING 
    Working effectively with others as a member of a team, group, organisation, and community during:
  • Class investigation, projects and groupwork. 
    		•

    UNIT STANDARD CCFO ORGANISING 
    Organising and managing oneself and one's activities responsibly and effectively when:
  • Doing investigations and projects. 
    		•

    UNIT STANDARD CCFO COLLECTING 
    Collecting, analysing, organising and critically evaluating information to better understand and explain:
  • Interpret information in order to develop a corresponding mathematical model (graph) of the context. 
    		•

    UNIT STANDARD CCFO COMMUNICATING 
    Communicating effectively using visual, mathematical and/or language skills in the modes of oral and/or written persuasion when:
  • Use everyday language and mathematical language and symbols to describe processes, theorems and in solving mathematical problems. 
    		•

    UNIT STANDARD CCFO SCIENCE 
    Using science and technology effectively and critically, showing responsibility towards the environment and health of others when:
  • Represent information in a matrix.
  • Solve simple network problems deriving algorithms for weighted graphs. 
    		•

    UNIT STANDARD CCFO DEMONSTRATING 
    Demonstrating an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation when:
  • Recognising that mathematical argument, proof and problem-solving do not exist in isolation of the broader mathematical community and the applications of mathematical in a social world. 
    		•

    UNIT STANDARD ASSESSOR CRITERIA 
    N/A 

    REREGISTRATION HISTORY 
    As per the SAQA Board decision/s at that time, this unit standard was Reregistered in 2012; 2015. 

    UNIT STANDARD NOTES 
    N/A 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Fundamental  63589   National Diploma: Geographical Information Science  Level 5  NQF Level 05  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  CETA 
    Elective  65649   National Certificate: Official Statistics  Level 5  Level TBA: Pre-2009 was L5  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  PSETA 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS UNIT STANDARD: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    NONE 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.