This course aims to equip students with the fundamental concepts of linear algebra and their computational applications. The goal is to develop skills to solve systems of linear equations using matrices and determinants, and to understand the structural properties of vector spaces, subspaces, basis, and dimension. Students will explore inner product spaces and the Gram-Schmidt process, progressing to linear transformations. The course will also cover eigenvalues, eigenvectors, and diagonalization to provide the necessary mathematical framework for analyzing engineering systems.
Upon successful completion of this course, students will be able to:
1.Solve systems of linear equations using matrix algebra and properties of determinants,
2.Analyze vector spaces and subspaces to determine linear independence, basis, and dimension,
3.Construct orthogonal and orthonormal bases in inner product spaces using the Gram-Schmidt process,
4.Identify linear transformations and their corresponding matrix representations,
5.Compute eigenvalues and eigenvectors to diagonalize matrices.