First Semester

Introduction to Systems of Linear Equations, Gaussian Elimination, Homogeneous Systems, Matrices and Matrix Operations, Rules of Matrix Arithmetic, Different Methods of Finding the Inverse, Determinant, Properties of Determinant Function, Cofactor Expansion, Cramer's Rule,

Vectors in 2D and 3D Spaces, Norm, Dot Product, Projection, Cross Product, Lines and Planes,

Vector Spaces, Subspaces, Linear Independence.

Second Semester

Basis, Dimension, Orthonormal Basis, Gram-Schmidt Process, Change of Basis,

Linear Transformations, Kernel, Range, Matrices of Linear Transformations, Similarity, Eigenvalues, Eigenvectors, Diagonalisation of Matrices, Symmetric Matrices.