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HE Unit Template
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Linear Algebra and Applications
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GPMAT1102 - Linear Algebra and Applications
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20240200
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Course
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Unit
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1.3
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2026-09-10
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2026-09-10
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Engineering
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Institute of Innovation, Science & Sustainability
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Engineering
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Undergraduate
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15
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.125
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010101
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Mathematics
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010101 - Mathematics
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<a href="http://www.federation.edu.au/locate/unit/gpmat1102">View unit fees</a>
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Graded (e.g. HD, D, C, etc)
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5
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Diploma, Undergraduate Certificate
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<p>This course offers students an introduction to the use of mathematical methods in finding optimal choices in business, industry, economics, and social, behavioural and biological sciences. It introduces students to linear algebra and linear programming that underlie applications in operations research.</p>
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<p>This may include:<br>
•Matrix representations of systems of linear equations;<br>
•Vectors and matrices and their algebraic properties;<br>
•Determinants and inverses of matrices;<br>
•Dot products and cross products of vectors;<br>
•Lines and planes in 3-space;<br>
•Vector spaces, linear independence, basis, dimension and rank of matrices;<br>
•Inner products, orthonormal bases, orthogonal matrices;<br>
•Diagonalization of matrices, eigenvalues and eigenvectors;<br>
•The setting of LP problems and the geometry of LP problems<br>
•The Simplex algorithm;<br>
•Duality;<br>
•Modern algorithms such as those based on interior point methods;<br>
•Transportation problems;<br>
•Network flow problems;<br>
•Applications of LP;<br>
•Software packages for solving LP problems.</p>
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<p>Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment.</p>
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2027
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2026
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GPMAT1102 - Linear Algebra and Applications
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GPMAT1102 - Linear Algebra and Applications
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Semester 1
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Year
2027
2026
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Overview
Key information
Requisites
Learning outcomes
Assessment
Parent Region
Overview
Unit description
<p>This course offers students an introduction to the use of mathematical methods in finding optimal choices in business, industry, economics, and social, behavioural and biological sciences. It introduces students to linear algebra and linear programming that underlie applications in operations research.</p>
Unit content
<p>This may include:<br> •Matrix representations of systems of linear equations;<br> •Vectors and matrices and their algebraic properties;<br> •Determinants and inverses of matrices;<br> •Dot products and cross products of vectors;<br> •Lines and planes in 3-space;<br> •Vector spaces, linear independence, basis, dimension and rank of matrices;<br> •Inner products, orthonormal bases, orthogonal matrices;<br> •Diagonalization of matrices, eigenvalues and eigenvectors;<br> •The setting of LP problems and the geometry of LP problems<br> •The Simplex algorithm;<br> •Duality;<br> •Modern algorithms such as those based on interior point methods;<br> •Transportation problems;<br> •Network flow problems;<br> •Applications of LP;<br> •Software packages for solving LP problems.</p>
Key information
Institute / school:
Institute of Innovation, Science & Sustainability
Discipline:
Engineering
Study level:
Undergraduate
Credit points:
15
EFTSL:
0.125
Field of education:
010101 - Mathematics
Grade scheme:
Graded (e.g. HD, D, C, etc)
Placement component:
No
Fee information:
<a href="http://www.federation.edu.au/locate/unit/gpmat1102">View unit fees</a>
Requisites
Prerequisite
None
Corequisite
None
Exclusion
None
Learning outcomes
Learning outcomes
<p>On successful completion of this unit, students are expected to gain the following [K]nowledge, [S]kills and [A]pplication of knowledge & skills</p>
Learning Outcomes
Ref
Outcome
K1
<p>Recognise the fundamental structure of matrices and matrix arithmetic</p>
K2
<p>Explain the nature of vectors</p>
K3
<p>Recognise the basic techniques used for problems in linear programming</p>
K4
<p>Demonstrate an understanding of the theoretical basis for such algorithms.</p>
S1
<p>Represent and solve systems of linear equations;</p>
S2
<p>Perform the operations of addition, multiplication, and transposition of matrices;</p>
S3
<p>Find the determinant and inverse of a matrix;</p>
S4
<p>Prove simple algebraic statements about vector addition, scalar multiplication and inner products;</p>
S5
<p>Use vectors and operations involving vectors to solve problems involving lines and planes in 3-space;</p>
S6
<p>Find eigenvalues and eigenvectors of a 2x2 matrix;</p>
S7
<p>Graphically represent linear programming problems in 2 dimensions;</p>
S8
<p>Develop the appropriate English language and academic skills to successfully study at an undergraduate level.</p>
A1
<p>Use appropriate algorithms to solve linear programming problems;</p>
A2
<p>Use appropriate software packages to solve elementary problems of linear programming;</p>
Assessment
Learning Tasks and Assessment
Supplementary assessment available:
Yes
Supplementary assessment information:
<p>Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment.</p>
Key information
Institute / school:
Institute of Innovation, Science & Sustainability
Discipline:
Engineering
Study level:
Undergraduate
Credit points:
15
EFTSL:
0.125
Field of education:
010101 - Mathematics
Grade scheme:
Graded (e.g. HD, D, C, etc)
Placement component:
No
Fee information:
<a href="http://www.federation.edu.au/locate/unit/gpmat1102">View unit fees</a>
Additional information
Add Info Static Text
Internal reference: GPMAT1102 - U1.3