Course info

This course introduces fundamental concepts of matrix algebra and three-dimensional (3D) geometry, which are essential tools in engineering analysis, computer science, and applied mathematics.

The first part of the course focuses on matrices and linear algebra, including definitions, types of matrices, and fundamental operations such as addition, subtraction, and multiplication. Students will learn important concepts such as determinants, adjoint, inverse of a matrix, and methods for solving systems of linear equations (including Gaussian elimination and matrix inversion techniques). The course also introduces eigenvalues and eigenvectors, along with their applications in engineering problems and transformations.

The second part covers three-dimensional geometry, emphasizing the representation and analysis of geometric objects in space. Topics include coordinates in 3D, direction cosines and direction ratios, equations of straight lines and planes, and their relative positions. Students will study angles between lines and planes, conditions for parallelism and perpendicularity, and distances between points, lines, and planes. The course also introduces the standard equation and properties of spheres.

By the end of the course, students will be able to:

• Perform matrix operations and solve systems of linear equations
• Compute determinants, inverses, eigenvalues, and eigenvectors
• Analyze geometric objects in three-dimensional space
• Solve problems involving lines, planes, and spheres
• Apply mathematical concepts to engineering and computational problems

This course provides a strong mathematical foundation for advanced topics in engineering, computer graphics, data science, and numerical methods.