University • MTH 204 • NUC CCMAS

MTH 204: Linear Algebra I

Master the algebraic structures that underpin modern science and computation. This academic track delivers the complete NUC CCMAS MTH 204 curriculum, moving rigorously from abstract vector spaces to practical matrix theory. It provides the essential mathematical toolkit required for advanced problem-solving in high-demand STEM fields. This programme is targeted at undergraduates in mathematics, engineering, and computer science requiring a firm grounding in linear structures. It also serves professionals in data science, cryptography, and machine learning needing a rigorous theoretical refresher on foundational concepts. You will achieve competence in manipulating abstract vector spaces, determining basis and dimension, and analyzing linear transformations through their kernels and images. You will master matrix arithmetic, compute determinants, solve systems of linear equations using advanced methods, and apply techniques of eigenvalues and diagonalization. Completion establishes the critical foundation demanded for advanced studies in multivariate calculus, differential equations, and complex computational algorithms.

71 hrs

Enrolment valid for 12 months

Learning Track Courses

Linear Vector Spaces - Linear Algebra (Undergraduate Advanced)
Linear Vector Spaces - Linear Algebra (Undergraduate Advanced)
Do you want to learn how to work with abstract spaces and transformations that preserve their structure? Do you want to understand the concepts of vector subspaces, linear combinations, linear dependence, basis, dimension, coordinates, and properties of vector spaces? Do you want to master the skills of defining and manipulating linear maps, their kernels, images, matrix representations, and transition matrices? If you answered yes to any of these questions, then this course is for you! Linear Algebra: Linear Vector Spaces and Linear Maps is a comprehensive and engaging course that covers the fundamentals of vector spaces and linear maps and their applications in mathematics and science. You will learn how to: - Define and classify vector spaces and their subspaces over a given scalar field - Perform operations on vectors using linear combinations and scalar multiplication - Determine whether a set of vectors is linearly dependent or independent and find a basis and dimension for a vector space or subspace - Find the coordinates of a vector with respect to a given basis and change the basis using transition matrices - Define and classify linear maps between vector spaces and find their domains, codomains, ranges, and null spaces - Find the kernel and image of a linear map and use them to determine whether a linear map is one-to-one or onto - Represent a linear map using a matrix and perform matrix operations such as addition, multiplication, and inversion - Use different methods and tools to solve systems of linear equations, such as Gaussian elimination, row reduction, and inverse matrices This course is suitable for anyone who wants to learn or review the basics of vector spaces and linear maps and their applications. It is especially useful for students and professionals in algebra, geometry, analysis, differential equations, optimization, cryptography, computer graphics, data science, and other related fields. By the end of this course, you will have a solid foundation of the theory and practice of vector spaces and linear maps and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vector spaces and linear maps. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Do you want to learn how to work with abstract spaces and transformations that preserve their structure? Do you want to understand the concepts of vector subspaces, linear combinations, linear dependence, basis, dimension, coordinates, and properties of vector spaces? Do you want to master the skills of defining and manipulating linear maps, their kernels, images, matrix representations, and transition matrices? If you answered yes to any of these questions, then this course is for you! Linear Algebra: Linear Vector Spaces and Linear Maps is a comprehensive and engaging course that covers the fundamentals of vector spaces and linear maps and their applications in mathematics and science. You will learn how to: - Define and classify vector spaces and their subspaces over a given scalar field - Perform operations on vectors using linear combinations and scalar multiplication - Determine whether a set of vectors is linearly dependent or independent and find a basis and dimension for a vector space or subspace - Find the coordinates of a vector with respect to a given basis and change the basis using transition matrices - Define and classify linear maps between vector spaces and find their domains, codomains, ranges, and null spaces - Find the kernel and image of a linear map and use them to determine whether a linear map is one-to-one or onto - Represent a linear map using a matrix and perform matrix operations such as addition, multiplication, and inversion - Use different methods and tools to solve systems of linear equations, such as Gaussian elimination, row reduction, and inverse matrices This course is suitable for anyone who wants to learn or review the basics of vector spaces and linear maps and their applications. It is especially useful for students and professionals in algebra, geometry, analysis, differential equations, optimization, cryptography, computer graphics, data science, and other related fields. By the end of this course, you will have a solid foundation of the theory and practice of vector spaces and linear maps and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vector spaces and linear maps. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Linear Maps (Transformations) - Linear Algebra (Undergraduate Advanced)
Linear Maps (Transformations) - Linear Algebra (Undergraduate Advanced)
A comprehensive study of linear transformations (or maps) - definition, kernel, range, matrix representation and related matters.

A comprehensive study of linear transformations (or maps) - definition, kernel, range, matrix representation and related matters.

Matrices, Determinants, and Systems of Linear Equations - Linear Algebra (Undergraduate Advanced)
Matrices, Determinants, and Systems of Linear Equations - Linear Algebra (Undergraduate Advanced)
Master advanced matrix algebra and linear systems through rigorous technical training. This course covers matrix definitions; algebraic operations; transpositions; and elementary row transformations. You will investigate determinants; matrix inverses using the adjoint method; and the structural properties of similar matrices. Computational methods using MS-Excel or Google Sheets are included to handle large-scale data sets efficiently. These mathematical structures are the engines behind modern engineering and data science. Structural engineers use matrices to calculate stress in bridges; computer scientists use them to render 3D graphics; and economists use linear systems to model market equilibrium. Mastering these tools allows you to solve multi-variable problems that are impossible to handle manually. By the end, you will possess the skills to execute matrix additions; multiplications; and scalar operations with absolute precision. You will demonstrate competence in reducing matrices to row echelon form; calculating rank and nullity; and evaluating determinants of any order. Furthermore, you will command the ability to solve complex systems of linear equations using Cramer's rule or matrix inversion; identify special matrix types like orthogonal or symmetric; and automate these calculations using software. This curriculum is built for undergraduate students in engineering; mathematics; and physics requiring a high-level command of linear algebra. Professionals in data science or finance will find the content vital for understanding the algorithms governing their software. Even those in general sciences will benefit from the structured logical thinking and numerical methods required to manage complex variables in any technical field.

Master advanced matrix algebra and linear systems through rigorous technical training. This course covers matrix definitions; algebraic operations; transpositions; and elementary row transformations. You will investigate determinants; matrix inverses using the adjoint method; and the structural properties of similar matrices. Computational methods using MS-Excel or Google Sheets are included to handle large-scale data sets efficiently. These mathematical structures are the engines behind modern engineering and data science. Structural engineers use matrices to calculate stress in bridges; computer scientists use them to render 3D graphics; and economists use linear systems to model market equilibrium. Mastering these tools allows you to solve multi-variable problems that are impossible to handle manually. By the end, you will possess the skills to execute matrix additions; multiplications; and scalar operations with absolute precision. You will demonstrate competence in reducing matrices to row echelon form; calculating rank and nullity; and evaluating determinants of any order. Furthermore, you will command the ability to solve complex systems of linear equations using Cramer's rule or matrix inversion; identify special matrix types like orthogonal or symmetric; and automate these calculations using software. This curriculum is built for undergraduate students in engineering; mathematics; and physics requiring a high-level command of linear algebra. Professionals in data science or finance will find the content vital for understanding the algorithms governing their software. Even those in general sciences will benefit from the structured logical thinking and numerical methods required to manage complex variables in any technical field.