**Synopsis:**

The course begins with the study of matrices and determinant. Starting with simple matrix operations, elementary row operation and inverses, and determinant of matrices. Solve the linear system using Inverse of matrix, Crammer’s rule, Gauss and Gauss-Jordan elimination method. Next, the focus is on the vector spaces, subspace, linear independence, spanning sets, bases, coordinate vector and change of basis, orthogonal bases, and the Gram-Schmidt process. Next, a discussion of linear transformation and matrices, as well as the kernel and range is studied. Finally, finding the eigenvalues and eigenvectors and use them in diagonalization problem.

**Objectives:**

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

- Identity the type of matrices, perform the elementary row operation (ERO) and determine the determinant and inverse of matrices.
- Solve a system of linear equation by various methods and determine the existence and type of solutions of a given system of linear equations.
- Determine whether the given set is a vector space or a subspace, and explain the concept of linear combination of vector, linearly independent, spanning set, basis and dimension.
- Determine whether the given transformation is a linear transformation, and able to find the range and kernel of a given linear transformations.
- Find the eigenvalues and eigenvectors and use them in diagonalization problem.