Definition of matrices: addition and scalar multiplication, matrix multiplication, transpose of matrix, symmetric matrix, skewed symmetric matrix, diagonal matrix and identity matrix. Elementary row operation, reduced row-echelon form, singular matrix and nonsingular matrix, inverse of a matrix.

Systems of linear equations: solving by matrix method, homogeneous systems of linear equations, geometrical representation, solutions to AX=B with two unknowns.



Determinant of a square matrix, cofactor, finding determinant by using cofactors, properties of determinant and adjoint of a matrix. Relationship between adjoint and determinant of square matrices. Finding inverses of matrices using determinants, Cramers rule, eigenvalues and eigenvectors.



Vector spaces, subspaces, basis and dimension, addition of spaces, isomorphic vector spaces.

Linear transformation, definition and its properties. Matrix representation of a linear transformation, kernel and range, change of basis. Inner product. Gram-Schmidt process and projection. Innerproduct space, orthorgonal set and orthonormal basis.



References:

1. Kolman, B. & Hill, D.R. (2004). Elementary Linear Algebra (8th Edition). Pearson Education Inc.

2. Anton, H. (2005). Elementary Linear Algebra (9th Edition). John Wiley & Sons.

3. Leon, S.J. (2006). Linear Algebra with Application (7th Edition). Pearson Education Inc.