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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