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Main
UQU Programs

Linear Algebra 1

MTH1401
4 hours English

Linear Algebra 1

Linear Algebra 1
1 Linear Equations and Systems: / System of linear equations / Solutions: consistent, inconsistent, unique, infinite solutions / Row eeduction and echelon forms / Gaussian and Gauss-Jordan elimination
2 Matrices and Determinants: / Definintion and types of matrices (square, diagonal, identity, elementary, etc.) / Matrix operation: addition, multiplication, scalar multiplication / Transpose of of a matrix / Determinants: properties, computation, and applications / Minors and Cofactors / Inverse of a matrix (via adjoint or row reduction)
3 Vecors and Vector Spaces: / Definition of vectors / Operations: addition, scalar multiplication / Vector spaces and subspaces / Linear cominations and spans / Basis and dimension
4 Linear Independence / Definition of linear idependence and dependence / Relation to basis and spans
5 Linear Transformations / Definitions and examples / Kernal and range
6 Eigenvalues and eigenvectors: / Definition and properties / Characteristic polynomial
7 Others: Revision and activities, Exam, quizzes
1.1 Mapped to: K1

Solve systems of linear equations using substituting, elimination methods, matrix representation AX=b, and row reduction techniques.

Teaching Strategy K1
Assessment Methods Lectures
1.2 Mapped to: K2

Compute inverses and determinants of matrices using different methods.

Teaching Strategy K2
Assessment Methods Lectures
1.4 Mapped to: K2

Recognize vector spaces, subspaces, and their properties. Characterize linearly independent vectors, linearly dependent vectors, and spanning property of sets of vectors, find a transition matrix between bases, and compute a basis and the dimension of a vector space.

Teaching Strategy K2
Assessment Methods Lectures
1.5 Mapped to: K1

Compute the matrix representation of a linear transformation, kernal and range of a transformation.

Teaching Strategy K1
Assessment Methods Lectures
1.6 Mapped to: K2

Calculate the characteristic polynomial of a matrix and find its eigenvalues, eigenvectors, and eigenspace.

Teaching Strategy K2
Assessment Methods Lectures
2.1 Mapped to: S1

Apply mathematical concepts, techniques and theorems to solve problems.

Teaching Strategy S1
Assessment Methods Lectures
2.2 Mapped to: S7

Use appropriate mathematical formulas and techniques to process the information and draw the relevant conclusion.

Teaching Strategy S7
Assessment Methods Lectures
3.1 Mapped to: Train students to think abstractly and logically, enabling them to approach complex problems systematically and to develop a structured problem-solving mindest.

Train students to think abstractly and logically, enabling them to approach complex problems systematically and to develop a structured problem-solving mindest.

Teaching Strategy V1
Assessment Methods Lectures
3.2 Mapped to: Provides a universal language for interdisciplinary collaboration: Engineers, data scientists, economists, and physicists often use linear algebra concepts to communicate and solve problems together effectively.

Provides a universal language for interdisciplinary collaboration: Engineers, data scientists, economists, and physicists often use linear algebra concepts to communicate and solve problems together effectively.

Teaching Strategy V2
Assessment Methods Lectures
Assessment
Weight
Midterm exam
30%
Homework and assignments
20%
Final Exam
50%
Total
100%