Linear Algebra

 




Matrices and Determinants:

Notion of matrix. Type of matrices. Algebra of matrics. Determinant function. Properties of  determinants. Minors, Cofactors, epansion and evaluation of determinants. Elementary row and colum operations and row reduced cehelon matrices. Invertible matriees  Different types of matrices, Rank of matrices.

Vectors in Rn and Cn: Review of geometric vectors in R2 and R3 spaces. Vectors in Rn and Cn. Inner product. Norm and distance in Rn and Cn.

System of Linear Equations: System of linear equations (homogeneous and non-homogeneous) and their solutions. Application of matrices and determinants for solving system of linear equations. Applications of system of equations in real life problems.

Vector Space: Nation of groups and fields. Vector spaces. Subspaces. Linear combination of vectors. Linear dependence of vectors. Basis and dimension of vector spaces. Row and column space of matrix. Rank of matrices. Solution spaces of systems of linear equations.

Linear Transformation: Linear transformations. Kernel and image of  linear transformation and their properties. Matrix representation of linear transformations. Change of bases.

Eigenvalues and Eigenvectors: Eigenvalues and Eigenvectors. Diagonalization. Cayley-Hamilton theorem and its application.

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